X757770101
X7577701
AHFOR OFFICIAL USE
Fill in these boxes and read what is printed below
Number of seat
Town
copy
Mark
Full name of centre
Forename(s) Surname
Scottish candidate numberDate of birth
YearDay Month
NationalQualications2016
Total marks mdash 140
Attempt ALL questions
Reference may be made to the Physics Relationships Sheet X7577711 and the Data Sheet on Page 02
Write your answers clearly in the spaces provided in this booklet Additional space for answers and rough work is provided at the end of this booklet If you use this space you must clearly identify the question number you are attempting Any rough work must be written in this booklet You should score through your rough work when you have written your final copy
Care should be taken to give an appropriate number of significant figures in the final answers to calculations
Use blue or black ink
Before leaving the examination room you must give this booklet to the Invigilator if you do not you may lose all the marks for this paper
X7577701
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Physics
X757770102Page 02
DATA SHEETCOMMON PHYSICAL QUANTITIES
Quantity Symbol Value Quantity Symbol Value
Gravitational acceleration on EarthRadius of EarthMass of EarthMass of MoonRadius of MoonMean Radius of Moon OrbitSolar radiusMass of Sun1 AUStefan-Boltzmann constantUniversal constant of gravitation
gREMEMMRM
σ
G
9middot8 m sminus2
6middot4 times 106 m6middot0 times 1024 kg7middot3 times 1022 kg1middot7 times 106 m
3middot84 times 108 m6middot955 times 108 m2middot0 times 1030 kg1middot5 times 1011 m
5middot67 times 10minus8 W mminus2 Kminus4
6middot67 times 10minus11 m3 kgminus1 sminus2
Mass of electronCharge on electronMass of neutronMass of protonMass of alpha particleCharge on alpha particlePlanckrsquos constantPermittivity of free spacePermeability of free spaceSpeed of light in vacuumSpeed of sound in air
meemnmpmα
h
ε0
μ0
c
v
9middot11 times 10minus31 kgminus1middot60 times 10minus19 C1middot675 times 10minus27 kg1middot673 times 10minus27 kg6middot645 times 10minus27 kg
3middot20 times 10minus19 C6middot63 times 10minus34 J s
8middot85 times 10minus12 F mminus1
4π times 10minus7 H mminus1
3middot0 times 108 m sminus1
3middot4 times 102 m sminus1
REFRACTIVE INDICESThe refractive indices refer to sodium light of wavelength 589 nm and to substances at a temperature of 273 K
Substance Refractive index Substance Refractive index
DiamondGlassIcePerspex
2middot421middot51 1middot311middot49
GlycerolWaterAirMagnesium Fluoride
1middot47 1middot331middot001middot38
SPECTRAL LINES
Element Wavelengthnm Colour Element Wavelengthnm Colour
Hydrogen
Sodium
656486434410397389
589
RedBlue-greenBlue-violetVioletUltravioletUltraviolet
Yellow
Cadmium 644509480
RedGreenBlue
LasersElement Wavelengthnm Colour
Carbon dioxide
Helium-neon
955010590
633
Infrared
Red
PROPERTIES OF SELECTED MATERIALS
Substance Densitykg mminus3
MeltingPoint
K
BoilingPoint
K
Specific HeatCapacityJ kgminus1 Kminus1
Specific LatentHeat ofFusionJ kgminus1
Specific LatentHeat of
VaporisationJ kgminus1
AluminiumCopperGlassIceGlycerolMethanolSea WaterWaterAirHydrogenNitrogenOxygen
2middot70 times 103
8middot96 times 103
2middot60 times 103
9middot20 times 102
1middot26 times 103
7middot91 times 102
1middot02 times 103
1middot00 times 103
1middot299middot0 times 10minus2
1middot251middot43
93313571400273291175264273
146355
26232853 563338377373
207790
9middot02 times 102
3middot86 times 102
6middot70 times 102
2middot10 times 103
2middot43 times 103
2middot52 times 103
3middot93 times 103
4middot19 times 103
1middot43 times 104
1middot04 times 103
9middot18 times 102
3middot95 times 105
2middot05 times 105
3middot34 times 105
1middot81 times 105
9middot9 times 104
3middot34 times 105
8middot30 times 105
1middot12 times 106
2middot26 times 106
4middot50 times 105
2middot00 times 105
2middot40 times 104
The gas densities refer to a temperature of 273 K and a pressure of 1middot01 times 105 Pa
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Total marks mdash 140 marks
Attempt ALL questions
1
A car on a long straight track accelerates from rest The carrsquos run begins at time t = 0
Its velocity v at time t is given by the equation
20 135 1 26v t tsdot sdot= +
where v is measured in m sminus1 and t is measured in s
Using calculus methods
(a) determine the acceleration of the car at t = 15middot0 s
Space for working and answer
(b) determine the displacement of the car from its original position at this time
Space for working and answer
3
3
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2 (a) An ideal conical pendulum consists of a mass moving with constant speed in a circular path as shown in Figure 2A
mass
Figure 2A
ω
(i) Explain why the mass is accelerating despite moving with constant speed
(ii) State the direction of this acceleration
1
1
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2 (continued)
(b) Swingball is a garden game in which a ball is attached to a light string connected to a vertical pole as shown in Figure 2B
The motion of the ball can be modelled as a conical pendulum
The ball has a mass of 0middot059 kg
Figure 2B
r
(i) The ball is hit such that it moves with constant speed in a horizontal circle of radius 0middot48 m
The ball completes 1middot5 revolutions in 2middot69 s
(A) Show that the angular velocity of the ball is 3middot5 rad sminus1
Space for working and answer
(B) Calculate the magnitude of the centripetal force acting on the ball
Space for working and answer
2
3
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2 (b) (i) (continued)
(C) The horizontal component of the tension in the string provides this centripetal force and the vertical component balances the weight of the ball
Calculate the magnitude of the tension in the string
Space for working and answer
(ii) The string breaks whilst the ball is at the position shown in Figure 2C
r
Figure 2C
ω
On Figure 2C draw the direction of the ballrsquos velocity immediately after the string breaks
(An additional diagram if required can be found on Page 39)
3
1
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3 A spacecraft is orbiting a comet as shown in Figure 3
The comet can be considered as a sphere with a radius of 2middot1 times 103 m and a mass of 9middot5 times 1012 kg
Figure 3 (not to scale)
(a) A lander was released by the spacecraft to land on the surface of the comet After impact with the comet the lander bounced back from the surface with an initial upward vertical velocity of 0middot38 m sminus1
By calculating the escape velocity of the comet show that the lander returned to the surface for a second time
Space for working and answer
[Turn over
4
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(b) (i) Show that the gravitational field strength at the surface of the comet is 1middot4 times 10minus4 N kgminus1
Space for working and answer
(ii) Using the data from the space mission a student tries to calculate the maximum height reached by the lander after its first bounce
The studentrsquos working is shown below
( )2 2
2 4
2
0 0 38 2 1 4 10
515 7
m
v u as
s
s
minussdot sdot
sdot
= +
= + times minus times times
=
The actual maximum height reached by the lander was not as calculated by the student
State whether the actual maximum height reached would be greater or smaller than calculated by the student
You must justify your answer
3
3
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4 Epsilon Eridani is a star 9middot94 times 1016 m from Earth It has a diameter of 1middot02 times 109 m The apparent brightness of Epsilon Eridani is measured on Earth to be 1middot05 times 10minus9 W mminus2
(a) Calculate the luminosity of Epsilon Eridani
Space for working and answer
(b) Calculate the surface temperature of Epsilon Eridani
Space for working and answer
(c) State an assumption made in your calculation in (b)
3
3
1
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5 Einsteinrsquos theory of general relativity can be used to describe the motion of objects in non-inertial frames of reference The equivalence principle is a key assumption of general relativity
(a) Explain what is meant by the terms
(i) non-inertial frames of reference
(ii) the equivalence principle
(b) Two astronauts are on board a spacecraft in deep space far away from any large masses When the spacecraft is accelerating one astronaut throws a ball towards the other
(i) On Figure 5A sketch the path that the ball would follow in the astronautsrsquo frame of reference
A B
spacecraftacceleratingin this direction
Figure 5A
(An additional diagram if required can be found on Page 39)
1
1
1
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(ii) The experiment is repeated when the spacecraft is travelling at constant speed
On Figure 5B sketch the path that the ball would follow in the astronautsrsquo frame of reference
spacecraftmoving ata constantspeedA B
Figure 5B
(An additional diagram if required can be found on Page 40)
(c) A clock is on the surface of the Earth and an identical clock is on board a spacecraft which is accelerating in deep space at 8 m sminus2
State which clock runs slower
Justify your answer in terms of the equivalence principle
[Turn over
1
2
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6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
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7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
3
1
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
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8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
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(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
3
3
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
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9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
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1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
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10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
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THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
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(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
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X757770102Page 02
DATA SHEETCOMMON PHYSICAL QUANTITIES
Quantity Symbol Value Quantity Symbol Value
Gravitational acceleration on EarthRadius of EarthMass of EarthMass of MoonRadius of MoonMean Radius of Moon OrbitSolar radiusMass of Sun1 AUStefan-Boltzmann constantUniversal constant of gravitation
gREMEMMRM
σ
G
9middot8 m sminus2
6middot4 times 106 m6middot0 times 1024 kg7middot3 times 1022 kg1middot7 times 106 m
3middot84 times 108 m6middot955 times 108 m2middot0 times 1030 kg1middot5 times 1011 m
5middot67 times 10minus8 W mminus2 Kminus4
6middot67 times 10minus11 m3 kgminus1 sminus2
Mass of electronCharge on electronMass of neutronMass of protonMass of alpha particleCharge on alpha particlePlanckrsquos constantPermittivity of free spacePermeability of free spaceSpeed of light in vacuumSpeed of sound in air
meemnmpmα
h
ε0
μ0
c
v
9middot11 times 10minus31 kgminus1middot60 times 10minus19 C1middot675 times 10minus27 kg1middot673 times 10minus27 kg6middot645 times 10minus27 kg
3middot20 times 10minus19 C6middot63 times 10minus34 J s
8middot85 times 10minus12 F mminus1
4π times 10minus7 H mminus1
3middot0 times 108 m sminus1
3middot4 times 102 m sminus1
REFRACTIVE INDICESThe refractive indices refer to sodium light of wavelength 589 nm and to substances at a temperature of 273 K
Substance Refractive index Substance Refractive index
DiamondGlassIcePerspex
2middot421middot51 1middot311middot49
GlycerolWaterAirMagnesium Fluoride
1middot47 1middot331middot001middot38
SPECTRAL LINES
Element Wavelengthnm Colour Element Wavelengthnm Colour
Hydrogen
Sodium
656486434410397389
589
RedBlue-greenBlue-violetVioletUltravioletUltraviolet
Yellow
Cadmium 644509480
RedGreenBlue
LasersElement Wavelengthnm Colour
Carbon dioxide
Helium-neon
955010590
633
Infrared
Red
PROPERTIES OF SELECTED MATERIALS
Substance Densitykg mminus3
MeltingPoint
K
BoilingPoint
K
Specific HeatCapacityJ kgminus1 Kminus1
Specific LatentHeat ofFusionJ kgminus1
Specific LatentHeat of
VaporisationJ kgminus1
AluminiumCopperGlassIceGlycerolMethanolSea WaterWaterAirHydrogenNitrogenOxygen
2middot70 times 103
8middot96 times 103
2middot60 times 103
9middot20 times 102
1middot26 times 103
7middot91 times 102
1middot02 times 103
1middot00 times 103
1middot299middot0 times 10minus2
1middot251middot43
93313571400273291175264273
146355
26232853 563338377373
207790
9middot02 times 102
3middot86 times 102
6middot70 times 102
2middot10 times 103
2middot43 times 103
2middot52 times 103
3middot93 times 103
4middot19 times 103
1middot43 times 104
1middot04 times 103
9middot18 times 102
3middot95 times 105
2middot05 times 105
3middot34 times 105
1middot81 times 105
9middot9 times 104
3middot34 times 105
8middot30 times 105
1middot12 times 106
2middot26 times 106
4middot50 times 105
2middot00 times 105
2middot40 times 104
The gas densities refer to a temperature of 273 K and a pressure of 1middot01 times 105 Pa
X757770103Page 03
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Total marks mdash 140 marks
Attempt ALL questions
1
A car on a long straight track accelerates from rest The carrsquos run begins at time t = 0
Its velocity v at time t is given by the equation
20 135 1 26v t tsdot sdot= +
where v is measured in m sminus1 and t is measured in s
Using calculus methods
(a) determine the acceleration of the car at t = 15middot0 s
Space for working and answer
(b) determine the displacement of the car from its original position at this time
Space for working and answer
3
3
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2 (a) An ideal conical pendulum consists of a mass moving with constant speed in a circular path as shown in Figure 2A
mass
Figure 2A
ω
(i) Explain why the mass is accelerating despite moving with constant speed
(ii) State the direction of this acceleration
1
1
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2 (continued)
(b) Swingball is a garden game in which a ball is attached to a light string connected to a vertical pole as shown in Figure 2B
The motion of the ball can be modelled as a conical pendulum
The ball has a mass of 0middot059 kg
Figure 2B
r
(i) The ball is hit such that it moves with constant speed in a horizontal circle of radius 0middot48 m
The ball completes 1middot5 revolutions in 2middot69 s
(A) Show that the angular velocity of the ball is 3middot5 rad sminus1
Space for working and answer
(B) Calculate the magnitude of the centripetal force acting on the ball
Space for working and answer
2
3
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2 (b) (i) (continued)
(C) The horizontal component of the tension in the string provides this centripetal force and the vertical component balances the weight of the ball
Calculate the magnitude of the tension in the string
Space for working and answer
(ii) The string breaks whilst the ball is at the position shown in Figure 2C
r
Figure 2C
ω
On Figure 2C draw the direction of the ballrsquos velocity immediately after the string breaks
(An additional diagram if required can be found on Page 39)
3
1
X757770107Page 07
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3 A spacecraft is orbiting a comet as shown in Figure 3
The comet can be considered as a sphere with a radius of 2middot1 times 103 m and a mass of 9middot5 times 1012 kg
Figure 3 (not to scale)
(a) A lander was released by the spacecraft to land on the surface of the comet After impact with the comet the lander bounced back from the surface with an initial upward vertical velocity of 0middot38 m sminus1
By calculating the escape velocity of the comet show that the lander returned to the surface for a second time
Space for working and answer
[Turn over
4
X757770108Page 08
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(b) (i) Show that the gravitational field strength at the surface of the comet is 1middot4 times 10minus4 N kgminus1
Space for working and answer
(ii) Using the data from the space mission a student tries to calculate the maximum height reached by the lander after its first bounce
The studentrsquos working is shown below
( )2 2
2 4
2
0 0 38 2 1 4 10
515 7
m
v u as
s
s
minussdot sdot
sdot
= +
= + times minus times times
=
The actual maximum height reached by the lander was not as calculated by the student
State whether the actual maximum height reached would be greater or smaller than calculated by the student
You must justify your answer
3
3
X757770109Page 09
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4 Epsilon Eridani is a star 9middot94 times 1016 m from Earth It has a diameter of 1middot02 times 109 m The apparent brightness of Epsilon Eridani is measured on Earth to be 1middot05 times 10minus9 W mminus2
(a) Calculate the luminosity of Epsilon Eridani
Space for working and answer
(b) Calculate the surface temperature of Epsilon Eridani
Space for working and answer
(c) State an assumption made in your calculation in (b)
3
3
1
[Turn over
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5 Einsteinrsquos theory of general relativity can be used to describe the motion of objects in non-inertial frames of reference The equivalence principle is a key assumption of general relativity
(a) Explain what is meant by the terms
(i) non-inertial frames of reference
(ii) the equivalence principle
(b) Two astronauts are on board a spacecraft in deep space far away from any large masses When the spacecraft is accelerating one astronaut throws a ball towards the other
(i) On Figure 5A sketch the path that the ball would follow in the astronautsrsquo frame of reference
A B
spacecraftacceleratingin this direction
Figure 5A
(An additional diagram if required can be found on Page 39)
1
1
1
X757770111Page 11
MARKS DO NOT WRITE IN
THIS MARGIN 5 (b) (continued)
(ii) The experiment is repeated when the spacecraft is travelling at constant speed
On Figure 5B sketch the path that the ball would follow in the astronautsrsquo frame of reference
spacecraftmoving ata constantspeedA B
Figure 5B
(An additional diagram if required can be found on Page 40)
(c) A clock is on the surface of the Earth and an identical clock is on board a spacecraft which is accelerating in deep space at 8 m sminus2
State which clock runs slower
Justify your answer in terms of the equivalence principle
[Turn over
1
2
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6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
X757770113Page 13
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7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
3
1
X757770114Page 14
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
X757770115Page 15
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THIS MARGIN
8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
X757770116Page 16
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
X757770117Page 17
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(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
3
3
X757770118Page 18
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
X757770119Page 19
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9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
X757770120Page 20
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
X757770121Page 21
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
[Turn over
1
2
X757770122Page 22
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
X757770123Page 23
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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THIS MARGIN
12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
MARKS DO NOT WRITE IN
THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
MARKS DO NOT WRITE IN
THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
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Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770103Page 03
MARKS DO NOT WRITE IN
THIS MARGIN
Total marks mdash 140 marks
Attempt ALL questions
1
A car on a long straight track accelerates from rest The carrsquos run begins at time t = 0
Its velocity v at time t is given by the equation
20 135 1 26v t tsdot sdot= +
where v is measured in m sminus1 and t is measured in s
Using calculus methods
(a) determine the acceleration of the car at t = 15middot0 s
Space for working and answer
(b) determine the displacement of the car from its original position at this time
Space for working and answer
3
3
[Turn over
X757770104Page 04
MARKS DO NOT WRITE IN
THIS MARGIN
2 (a) An ideal conical pendulum consists of a mass moving with constant speed in a circular path as shown in Figure 2A
mass
Figure 2A
ω
(i) Explain why the mass is accelerating despite moving with constant speed
(ii) State the direction of this acceleration
1
1
X757770105Page 05
MARKS DO NOT WRITE IN
THIS MARGIN
2 (continued)
(b) Swingball is a garden game in which a ball is attached to a light string connected to a vertical pole as shown in Figure 2B
The motion of the ball can be modelled as a conical pendulum
The ball has a mass of 0middot059 kg
Figure 2B
r
(i) The ball is hit such that it moves with constant speed in a horizontal circle of radius 0middot48 m
The ball completes 1middot5 revolutions in 2middot69 s
(A) Show that the angular velocity of the ball is 3middot5 rad sminus1
Space for working and answer
(B) Calculate the magnitude of the centripetal force acting on the ball
Space for working and answer
2
3
[Turn over
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MARKS DO NOT WRITE IN
THIS MARGIN
2 (b) (i) (continued)
(C) The horizontal component of the tension in the string provides this centripetal force and the vertical component balances the weight of the ball
Calculate the magnitude of the tension in the string
Space for working and answer
(ii) The string breaks whilst the ball is at the position shown in Figure 2C
r
Figure 2C
ω
On Figure 2C draw the direction of the ballrsquos velocity immediately after the string breaks
(An additional diagram if required can be found on Page 39)
3
1
X757770107Page 07
MARKS DO NOT WRITE IN
THIS MARGIN
3 A spacecraft is orbiting a comet as shown in Figure 3
The comet can be considered as a sphere with a radius of 2middot1 times 103 m and a mass of 9middot5 times 1012 kg
Figure 3 (not to scale)
(a) A lander was released by the spacecraft to land on the surface of the comet After impact with the comet the lander bounced back from the surface with an initial upward vertical velocity of 0middot38 m sminus1
By calculating the escape velocity of the comet show that the lander returned to the surface for a second time
Space for working and answer
[Turn over
4
X757770108Page 08
MARKS DO NOT WRITE IN
THIS MARGIN 3 (continued)
(b) (i) Show that the gravitational field strength at the surface of the comet is 1middot4 times 10minus4 N kgminus1
Space for working and answer
(ii) Using the data from the space mission a student tries to calculate the maximum height reached by the lander after its first bounce
The studentrsquos working is shown below
( )2 2
2 4
2
0 0 38 2 1 4 10
515 7
m
v u as
s
s
minussdot sdot
sdot
= +
= + times minus times times
=
The actual maximum height reached by the lander was not as calculated by the student
State whether the actual maximum height reached would be greater or smaller than calculated by the student
You must justify your answer
3
3
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4 Epsilon Eridani is a star 9middot94 times 1016 m from Earth It has a diameter of 1middot02 times 109 m The apparent brightness of Epsilon Eridani is measured on Earth to be 1middot05 times 10minus9 W mminus2
(a) Calculate the luminosity of Epsilon Eridani
Space for working and answer
(b) Calculate the surface temperature of Epsilon Eridani
Space for working and answer
(c) State an assumption made in your calculation in (b)
3
3
1
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5 Einsteinrsquos theory of general relativity can be used to describe the motion of objects in non-inertial frames of reference The equivalence principle is a key assumption of general relativity
(a) Explain what is meant by the terms
(i) non-inertial frames of reference
(ii) the equivalence principle
(b) Two astronauts are on board a spacecraft in deep space far away from any large masses When the spacecraft is accelerating one astronaut throws a ball towards the other
(i) On Figure 5A sketch the path that the ball would follow in the astronautsrsquo frame of reference
A B
spacecraftacceleratingin this direction
Figure 5A
(An additional diagram if required can be found on Page 39)
1
1
1
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THIS MARGIN 5 (b) (continued)
(ii) The experiment is repeated when the spacecraft is travelling at constant speed
On Figure 5B sketch the path that the ball would follow in the astronautsrsquo frame of reference
spacecraftmoving ata constantspeedA B
Figure 5B
(An additional diagram if required can be found on Page 40)
(c) A clock is on the surface of the Earth and an identical clock is on board a spacecraft which is accelerating in deep space at 8 m sminus2
State which clock runs slower
Justify your answer in terms of the equivalence principle
[Turn over
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6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
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7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
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8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
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THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
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9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
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1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
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10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
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4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
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1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
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2
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
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THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
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THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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2 (a) An ideal conical pendulum consists of a mass moving with constant speed in a circular path as shown in Figure 2A
mass
Figure 2A
ω
(i) Explain why the mass is accelerating despite moving with constant speed
(ii) State the direction of this acceleration
1
1
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2 (continued)
(b) Swingball is a garden game in which a ball is attached to a light string connected to a vertical pole as shown in Figure 2B
The motion of the ball can be modelled as a conical pendulum
The ball has a mass of 0middot059 kg
Figure 2B
r
(i) The ball is hit such that it moves with constant speed in a horizontal circle of radius 0middot48 m
The ball completes 1middot5 revolutions in 2middot69 s
(A) Show that the angular velocity of the ball is 3middot5 rad sminus1
Space for working and answer
(B) Calculate the magnitude of the centripetal force acting on the ball
Space for working and answer
2
3
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2 (b) (i) (continued)
(C) The horizontal component of the tension in the string provides this centripetal force and the vertical component balances the weight of the ball
Calculate the magnitude of the tension in the string
Space for working and answer
(ii) The string breaks whilst the ball is at the position shown in Figure 2C
r
Figure 2C
ω
On Figure 2C draw the direction of the ballrsquos velocity immediately after the string breaks
(An additional diagram if required can be found on Page 39)
3
1
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3 A spacecraft is orbiting a comet as shown in Figure 3
The comet can be considered as a sphere with a radius of 2middot1 times 103 m and a mass of 9middot5 times 1012 kg
Figure 3 (not to scale)
(a) A lander was released by the spacecraft to land on the surface of the comet After impact with the comet the lander bounced back from the surface with an initial upward vertical velocity of 0middot38 m sminus1
By calculating the escape velocity of the comet show that the lander returned to the surface for a second time
Space for working and answer
[Turn over
4
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(b) (i) Show that the gravitational field strength at the surface of the comet is 1middot4 times 10minus4 N kgminus1
Space for working and answer
(ii) Using the data from the space mission a student tries to calculate the maximum height reached by the lander after its first bounce
The studentrsquos working is shown below
( )2 2
2 4
2
0 0 38 2 1 4 10
515 7
m
v u as
s
s
minussdot sdot
sdot
= +
= + times minus times times
=
The actual maximum height reached by the lander was not as calculated by the student
State whether the actual maximum height reached would be greater or smaller than calculated by the student
You must justify your answer
3
3
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4 Epsilon Eridani is a star 9middot94 times 1016 m from Earth It has a diameter of 1middot02 times 109 m The apparent brightness of Epsilon Eridani is measured on Earth to be 1middot05 times 10minus9 W mminus2
(a) Calculate the luminosity of Epsilon Eridani
Space for working and answer
(b) Calculate the surface temperature of Epsilon Eridani
Space for working and answer
(c) State an assumption made in your calculation in (b)
3
3
1
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5 Einsteinrsquos theory of general relativity can be used to describe the motion of objects in non-inertial frames of reference The equivalence principle is a key assumption of general relativity
(a) Explain what is meant by the terms
(i) non-inertial frames of reference
(ii) the equivalence principle
(b) Two astronauts are on board a spacecraft in deep space far away from any large masses When the spacecraft is accelerating one astronaut throws a ball towards the other
(i) On Figure 5A sketch the path that the ball would follow in the astronautsrsquo frame of reference
A B
spacecraftacceleratingin this direction
Figure 5A
(An additional diagram if required can be found on Page 39)
1
1
1
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THIS MARGIN 5 (b) (continued)
(ii) The experiment is repeated when the spacecraft is travelling at constant speed
On Figure 5B sketch the path that the ball would follow in the astronautsrsquo frame of reference
spacecraftmoving ata constantspeedA B
Figure 5B
(An additional diagram if required can be found on Page 40)
(c) A clock is on the surface of the Earth and an identical clock is on board a spacecraft which is accelerating in deep space at 8 m sminus2
State which clock runs slower
Justify your answer in terms of the equivalence principle
[Turn over
1
2
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6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
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7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
3
1
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
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8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
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THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
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3
3
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
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9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
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4
2
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
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1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
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10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
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2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
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THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
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THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
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Page 08
[BLANK PAGE]
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X757770105Page 05
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2 (continued)
(b) Swingball is a garden game in which a ball is attached to a light string connected to a vertical pole as shown in Figure 2B
The motion of the ball can be modelled as a conical pendulum
The ball has a mass of 0middot059 kg
Figure 2B
r
(i) The ball is hit such that it moves with constant speed in a horizontal circle of radius 0middot48 m
The ball completes 1middot5 revolutions in 2middot69 s
(A) Show that the angular velocity of the ball is 3middot5 rad sminus1
Space for working and answer
(B) Calculate the magnitude of the centripetal force acting on the ball
Space for working and answer
2
3
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2 (b) (i) (continued)
(C) The horizontal component of the tension in the string provides this centripetal force and the vertical component balances the weight of the ball
Calculate the magnitude of the tension in the string
Space for working and answer
(ii) The string breaks whilst the ball is at the position shown in Figure 2C
r
Figure 2C
ω
On Figure 2C draw the direction of the ballrsquos velocity immediately after the string breaks
(An additional diagram if required can be found on Page 39)
3
1
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THIS MARGIN
3 A spacecraft is orbiting a comet as shown in Figure 3
The comet can be considered as a sphere with a radius of 2middot1 times 103 m and a mass of 9middot5 times 1012 kg
Figure 3 (not to scale)
(a) A lander was released by the spacecraft to land on the surface of the comet After impact with the comet the lander bounced back from the surface with an initial upward vertical velocity of 0middot38 m sminus1
By calculating the escape velocity of the comet show that the lander returned to the surface for a second time
Space for working and answer
[Turn over
4
X757770108Page 08
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THIS MARGIN 3 (continued)
(b) (i) Show that the gravitational field strength at the surface of the comet is 1middot4 times 10minus4 N kgminus1
Space for working and answer
(ii) Using the data from the space mission a student tries to calculate the maximum height reached by the lander after its first bounce
The studentrsquos working is shown below
( )2 2
2 4
2
0 0 38 2 1 4 10
515 7
m
v u as
s
s
minussdot sdot
sdot
= +
= + times minus times times
=
The actual maximum height reached by the lander was not as calculated by the student
State whether the actual maximum height reached would be greater or smaller than calculated by the student
You must justify your answer
3
3
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4 Epsilon Eridani is a star 9middot94 times 1016 m from Earth It has a diameter of 1middot02 times 109 m The apparent brightness of Epsilon Eridani is measured on Earth to be 1middot05 times 10minus9 W mminus2
(a) Calculate the luminosity of Epsilon Eridani
Space for working and answer
(b) Calculate the surface temperature of Epsilon Eridani
Space for working and answer
(c) State an assumption made in your calculation in (b)
3
3
1
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5 Einsteinrsquos theory of general relativity can be used to describe the motion of objects in non-inertial frames of reference The equivalence principle is a key assumption of general relativity
(a) Explain what is meant by the terms
(i) non-inertial frames of reference
(ii) the equivalence principle
(b) Two astronauts are on board a spacecraft in deep space far away from any large masses When the spacecraft is accelerating one astronaut throws a ball towards the other
(i) On Figure 5A sketch the path that the ball would follow in the astronautsrsquo frame of reference
A B
spacecraftacceleratingin this direction
Figure 5A
(An additional diagram if required can be found on Page 39)
1
1
1
X757770111Page 11
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THIS MARGIN 5 (b) (continued)
(ii) The experiment is repeated when the spacecraft is travelling at constant speed
On Figure 5B sketch the path that the ball would follow in the astronautsrsquo frame of reference
spacecraftmoving ata constantspeedA B
Figure 5B
(An additional diagram if required can be found on Page 40)
(c) A clock is on the surface of the Earth and an identical clock is on board a spacecraft which is accelerating in deep space at 8 m sminus2
State which clock runs slower
Justify your answer in terms of the equivalence principle
[Turn over
1
2
X757770112Page 12
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6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
X757770113Page 13
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7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
3
1
X757770114Page 14
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
X757770115Page 15
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THIS MARGIN
8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
X757770117Page 17
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THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
3
3
X757770118Page 18
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
X757770119Page 19
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9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
X757770120Page 20
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
X757770121Page 21
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
[Turn over
1
2
X757770122Page 22
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
X757770123Page 23
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
X757770124Page 24
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
X757770125Page 25
MARKS DO NOT WRITE IN
THIS MARGIN
11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
X757770126Page 26
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THIS MARGIN
12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
X757770127Page 27
MARKS DO NOT WRITE IN
THIS MARGIN
12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
X757770128Page 28
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
MARKS DO NOT WRITE IN
THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
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THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
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1
X757770134Page 34
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Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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X757770106Page 06
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2 (b) (i) (continued)
(C) The horizontal component of the tension in the string provides this centripetal force and the vertical component balances the weight of the ball
Calculate the magnitude of the tension in the string
Space for working and answer
(ii) The string breaks whilst the ball is at the position shown in Figure 2C
r
Figure 2C
ω
On Figure 2C draw the direction of the ballrsquos velocity immediately after the string breaks
(An additional diagram if required can be found on Page 39)
3
1
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3 A spacecraft is orbiting a comet as shown in Figure 3
The comet can be considered as a sphere with a radius of 2middot1 times 103 m and a mass of 9middot5 times 1012 kg
Figure 3 (not to scale)
(a) A lander was released by the spacecraft to land on the surface of the comet After impact with the comet the lander bounced back from the surface with an initial upward vertical velocity of 0middot38 m sminus1
By calculating the escape velocity of the comet show that the lander returned to the surface for a second time
Space for working and answer
[Turn over
4
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THIS MARGIN 3 (continued)
(b) (i) Show that the gravitational field strength at the surface of the comet is 1middot4 times 10minus4 N kgminus1
Space for working and answer
(ii) Using the data from the space mission a student tries to calculate the maximum height reached by the lander after its first bounce
The studentrsquos working is shown below
( )2 2
2 4
2
0 0 38 2 1 4 10
515 7
m
v u as
s
s
minussdot sdot
sdot
= +
= + times minus times times
=
The actual maximum height reached by the lander was not as calculated by the student
State whether the actual maximum height reached would be greater or smaller than calculated by the student
You must justify your answer
3
3
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4 Epsilon Eridani is a star 9middot94 times 1016 m from Earth It has a diameter of 1middot02 times 109 m The apparent brightness of Epsilon Eridani is measured on Earth to be 1middot05 times 10minus9 W mminus2
(a) Calculate the luminosity of Epsilon Eridani
Space for working and answer
(b) Calculate the surface temperature of Epsilon Eridani
Space for working and answer
(c) State an assumption made in your calculation in (b)
3
3
1
[Turn over
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5 Einsteinrsquos theory of general relativity can be used to describe the motion of objects in non-inertial frames of reference The equivalence principle is a key assumption of general relativity
(a) Explain what is meant by the terms
(i) non-inertial frames of reference
(ii) the equivalence principle
(b) Two astronauts are on board a spacecraft in deep space far away from any large masses When the spacecraft is accelerating one astronaut throws a ball towards the other
(i) On Figure 5A sketch the path that the ball would follow in the astronautsrsquo frame of reference
A B
spacecraftacceleratingin this direction
Figure 5A
(An additional diagram if required can be found on Page 39)
1
1
1
X757770111Page 11
MARKS DO NOT WRITE IN
THIS MARGIN 5 (b) (continued)
(ii) The experiment is repeated when the spacecraft is travelling at constant speed
On Figure 5B sketch the path that the ball would follow in the astronautsrsquo frame of reference
spacecraftmoving ata constantspeedA B
Figure 5B
(An additional diagram if required can be found on Page 40)
(c) A clock is on the surface of the Earth and an identical clock is on board a spacecraft which is accelerating in deep space at 8 m sminus2
State which clock runs slower
Justify your answer in terms of the equivalence principle
[Turn over
1
2
X757770112Page 12
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6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
X757770113Page 13
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7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
3
1
X757770114Page 14
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THIS MARGIN
7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
X757770115Page 15
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THIS MARGIN
8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
X757770116Page 16
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
X757770117Page 17
MARKS DO NOT WRITE IN
THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
3
3
X757770118Page 18
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
X757770119Page 19
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THIS MARGIN
9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
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4
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
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2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
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10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
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1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
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2
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
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THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
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2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
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THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770107Page 07
MARKS DO NOT WRITE IN
THIS MARGIN
3 A spacecraft is orbiting a comet as shown in Figure 3
The comet can be considered as a sphere with a radius of 2middot1 times 103 m and a mass of 9middot5 times 1012 kg
Figure 3 (not to scale)
(a) A lander was released by the spacecraft to land on the surface of the comet After impact with the comet the lander bounced back from the surface with an initial upward vertical velocity of 0middot38 m sminus1
By calculating the escape velocity of the comet show that the lander returned to the surface for a second time
Space for working and answer
[Turn over
4
X757770108Page 08
MARKS DO NOT WRITE IN
THIS MARGIN 3 (continued)
(b) (i) Show that the gravitational field strength at the surface of the comet is 1middot4 times 10minus4 N kgminus1
Space for working and answer
(ii) Using the data from the space mission a student tries to calculate the maximum height reached by the lander after its first bounce
The studentrsquos working is shown below
( )2 2
2 4
2
0 0 38 2 1 4 10
515 7
m
v u as
s
s
minussdot sdot
sdot
= +
= + times minus times times
=
The actual maximum height reached by the lander was not as calculated by the student
State whether the actual maximum height reached would be greater or smaller than calculated by the student
You must justify your answer
3
3
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4 Epsilon Eridani is a star 9middot94 times 1016 m from Earth It has a diameter of 1middot02 times 109 m The apparent brightness of Epsilon Eridani is measured on Earth to be 1middot05 times 10minus9 W mminus2
(a) Calculate the luminosity of Epsilon Eridani
Space for working and answer
(b) Calculate the surface temperature of Epsilon Eridani
Space for working and answer
(c) State an assumption made in your calculation in (b)
3
3
1
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5 Einsteinrsquos theory of general relativity can be used to describe the motion of objects in non-inertial frames of reference The equivalence principle is a key assumption of general relativity
(a) Explain what is meant by the terms
(i) non-inertial frames of reference
(ii) the equivalence principle
(b) Two astronauts are on board a spacecraft in deep space far away from any large masses When the spacecraft is accelerating one astronaut throws a ball towards the other
(i) On Figure 5A sketch the path that the ball would follow in the astronautsrsquo frame of reference
A B
spacecraftacceleratingin this direction
Figure 5A
(An additional diagram if required can be found on Page 39)
1
1
1
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THIS MARGIN 5 (b) (continued)
(ii) The experiment is repeated when the spacecraft is travelling at constant speed
On Figure 5B sketch the path that the ball would follow in the astronautsrsquo frame of reference
spacecraftmoving ata constantspeedA B
Figure 5B
(An additional diagram if required can be found on Page 40)
(c) A clock is on the surface of the Earth and an identical clock is on board a spacecraft which is accelerating in deep space at 8 m sminus2
State which clock runs slower
Justify your answer in terms of the equivalence principle
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6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
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7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
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8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
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THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
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9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
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1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
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10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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THIS MARGIN
11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
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4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
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1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
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THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
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THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
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3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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Page 08
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X757770108Page 08
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(b) (i) Show that the gravitational field strength at the surface of the comet is 1middot4 times 10minus4 N kgminus1
Space for working and answer
(ii) Using the data from the space mission a student tries to calculate the maximum height reached by the lander after its first bounce
The studentrsquos working is shown below
( )2 2
2 4
2
0 0 38 2 1 4 10
515 7
m
v u as
s
s
minussdot sdot
sdot
= +
= + times minus times times
=
The actual maximum height reached by the lander was not as calculated by the student
State whether the actual maximum height reached would be greater or smaller than calculated by the student
You must justify your answer
3
3
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4 Epsilon Eridani is a star 9middot94 times 1016 m from Earth It has a diameter of 1middot02 times 109 m The apparent brightness of Epsilon Eridani is measured on Earth to be 1middot05 times 10minus9 W mminus2
(a) Calculate the luminosity of Epsilon Eridani
Space for working and answer
(b) Calculate the surface temperature of Epsilon Eridani
Space for working and answer
(c) State an assumption made in your calculation in (b)
3
3
1
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5 Einsteinrsquos theory of general relativity can be used to describe the motion of objects in non-inertial frames of reference The equivalence principle is a key assumption of general relativity
(a) Explain what is meant by the terms
(i) non-inertial frames of reference
(ii) the equivalence principle
(b) Two astronauts are on board a spacecraft in deep space far away from any large masses When the spacecraft is accelerating one astronaut throws a ball towards the other
(i) On Figure 5A sketch the path that the ball would follow in the astronautsrsquo frame of reference
A B
spacecraftacceleratingin this direction
Figure 5A
(An additional diagram if required can be found on Page 39)
1
1
1
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THIS MARGIN 5 (b) (continued)
(ii) The experiment is repeated when the spacecraft is travelling at constant speed
On Figure 5B sketch the path that the ball would follow in the astronautsrsquo frame of reference
spacecraftmoving ata constantspeedA B
Figure 5B
(An additional diagram if required can be found on Page 40)
(c) A clock is on the surface of the Earth and an identical clock is on board a spacecraft which is accelerating in deep space at 8 m sminus2
State which clock runs slower
Justify your answer in terms of the equivalence principle
[Turn over
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2
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6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
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7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
3
1
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
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8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
X757770117Page 17
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THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
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3
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
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9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
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2
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
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1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
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10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
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4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
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2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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X757770109Page 09
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4 Epsilon Eridani is a star 9middot94 times 1016 m from Earth It has a diameter of 1middot02 times 109 m The apparent brightness of Epsilon Eridani is measured on Earth to be 1middot05 times 10minus9 W mminus2
(a) Calculate the luminosity of Epsilon Eridani
Space for working and answer
(b) Calculate the surface temperature of Epsilon Eridani
Space for working and answer
(c) State an assumption made in your calculation in (b)
3
3
1
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5 Einsteinrsquos theory of general relativity can be used to describe the motion of objects in non-inertial frames of reference The equivalence principle is a key assumption of general relativity
(a) Explain what is meant by the terms
(i) non-inertial frames of reference
(ii) the equivalence principle
(b) Two astronauts are on board a spacecraft in deep space far away from any large masses When the spacecraft is accelerating one astronaut throws a ball towards the other
(i) On Figure 5A sketch the path that the ball would follow in the astronautsrsquo frame of reference
A B
spacecraftacceleratingin this direction
Figure 5A
(An additional diagram if required can be found on Page 39)
1
1
1
X757770111Page 11
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THIS MARGIN 5 (b) (continued)
(ii) The experiment is repeated when the spacecraft is travelling at constant speed
On Figure 5B sketch the path that the ball would follow in the astronautsrsquo frame of reference
spacecraftmoving ata constantspeedA B
Figure 5B
(An additional diagram if required can be found on Page 40)
(c) A clock is on the surface of the Earth and an identical clock is on board a spacecraft which is accelerating in deep space at 8 m sminus2
State which clock runs slower
Justify your answer in terms of the equivalence principle
[Turn over
1
2
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6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
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THIS MARGIN
7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
3
1
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
X757770115Page 15
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THIS MARGIN
8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
X757770117Page 17
MARKS DO NOT WRITE IN
THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
3
3
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
X757770119Page 19
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9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
X757770121Page 21
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
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1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
X757770123Page 23
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
X757770125Page 25
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
MARKS DO NOT WRITE IN
THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
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Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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Page 08
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X757770110Page 10
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5 Einsteinrsquos theory of general relativity can be used to describe the motion of objects in non-inertial frames of reference The equivalence principle is a key assumption of general relativity
(a) Explain what is meant by the terms
(i) non-inertial frames of reference
(ii) the equivalence principle
(b) Two astronauts are on board a spacecraft in deep space far away from any large masses When the spacecraft is accelerating one astronaut throws a ball towards the other
(i) On Figure 5A sketch the path that the ball would follow in the astronautsrsquo frame of reference
A B
spacecraftacceleratingin this direction
Figure 5A
(An additional diagram if required can be found on Page 39)
1
1
1
X757770111Page 11
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THIS MARGIN 5 (b) (continued)
(ii) The experiment is repeated when the spacecraft is travelling at constant speed
On Figure 5B sketch the path that the ball would follow in the astronautsrsquo frame of reference
spacecraftmoving ata constantspeedA B
Figure 5B
(An additional diagram if required can be found on Page 40)
(c) A clock is on the surface of the Earth and an identical clock is on board a spacecraft which is accelerating in deep space at 8 m sminus2
State which clock runs slower
Justify your answer in terms of the equivalence principle
[Turn over
1
2
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6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
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THIS MARGIN
7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
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3
1
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
X757770115Page 15
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8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
X757770117Page 17
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THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
3
3
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
X757770119Page 19
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THIS MARGIN
9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
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THIS MARGIN
9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
X757770121Page 21
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
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1
2
X757770122Page 22
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
X757770123Page 23
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
X757770125Page 25
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THIS MARGIN
11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
X757770127Page 27
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
X757770128Page 28
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
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THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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Page 08
[BLANK PAGE]
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X757770111Page 11
MARKS DO NOT WRITE IN
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(ii) The experiment is repeated when the spacecraft is travelling at constant speed
On Figure 5B sketch the path that the ball would follow in the astronautsrsquo frame of reference
spacecraftmoving ata constantspeedA B
Figure 5B
(An additional diagram if required can be found on Page 40)
(c) A clock is on the surface of the Earth and an identical clock is on board a spacecraft which is accelerating in deep space at 8 m sminus2
State which clock runs slower
Justify your answer in terms of the equivalence principle
[Turn over
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6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
X757770113Page 13
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7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
X757770115Page 15
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8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
X757770117Page 17
MARKS DO NOT WRITE IN
THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
3
3
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THIS MARGIN
9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
X757770119Page 19
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THIS MARGIN
9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
X757770120Page 20
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THIS MARGIN
9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
X757770121Page 21
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THIS MARGIN
10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
[Turn over
1
2
X757770122Page 22
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THIS MARGIN
10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
X757770123Page 23
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
X757770125Page 25
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
X757770127Page 27
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770112Page 12
MARKS DO NOT WRITE IN
THIS MARGIN
6 A student makes the following statement
ldquoQuantum theory mdash I donrsquot understand it I donrsquot really know what it is I believe that classical physics can explain everythingrdquo
Use your knowledge of physics to comment on the statement 3
X757770113Page 13
MARKS DO NOT WRITE IN
THIS MARGIN
7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
3
1
X757770114Page 14
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
X757770115Page 15
MARKS DO NOT WRITE IN
THIS MARGIN
8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
X757770116Page 16
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THIS MARGIN
8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
X757770117Page 17
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THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
3
3
X757770118Page 18
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THIS MARGIN
9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
X757770119Page 19
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THIS MARGIN
9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
X757770120Page 20
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THIS MARGIN
9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
X757770121Page 21
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
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2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
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10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
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4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
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1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
MARKS DO NOT WRITE IN
THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
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3
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1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
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Do NoT wRiTE oN THiS PAGE
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
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3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770113Page 13
MARKS DO NOT WRITE IN
THIS MARGIN
7 (a) The Earth can be modelled as a black body radiator
The average surface temperature of the Earth can be estimated using the relationship
peak
bTλ
=
where
T is the average surface temperature of the Earth in kelvin
b is Wienrsquos Displacement Constant equal to 2middot89 times 10minus3 K m
λpeak is the peak wavelength of the radiation emitted by a black body radiator
The average surface temperature of Earth is 15 degC
(i) Estimate the peak wavelength of the radiation emitted by Earth
Space for working and answer
(ii) To which part of the electromagnetic spectrum does this peak wavelength correspond
[Turn over
3
1
X757770114Page 14
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THIS MARGIN
7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
X757770115Page 15
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THIS MARGIN
8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
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THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
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3
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
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THIS MARGIN
9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
[Turn over
1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
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THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
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THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
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Page 08
[BLANK PAGE]
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7 (continued)
(b) In order to investigate the properties of black body radiators a student makes measurements from the spectra produced by a filament lamp Measurements are made when the lamp is operated at its rated voltage and when it is operated at a lower voltage
The filament lamp can be considered to be a black body radiator
A graph of the results obtained is shown in Figure 7
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
(i) State which curve corresponds to the radiation emitted when the filament lamp is operating at its rated voltage
You must justify your answer
(ii) The shape of the curves on the graph on Figure 7 is not as predicted by classical physics
On Figure 7 sketch a curve to show the result predicted by classical physics
(An additional graph if required can be found on Page 40)
2
1
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8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
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THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
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3
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
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9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
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1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
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10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
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2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
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THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
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THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
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Do NoT wRiTE oN THiS PAGE
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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Page 08
[BLANK PAGE]
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X757770115Page 15
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8 Werner Heisenberg is considered to be one of the pioneers of quantum mechanics
He is most famous for his uncertainty principle which can be expressed in the equation
Δ Δ4xhx pπ
ge
(a) (i) State what quantity is represented by the term xpΔ
(ii) Explain the implications of the Heisenberg uncertainty principle for experimental measurements
[Turn over
1
1
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
X757770117Page 17
MARKS DO NOT WRITE IN
THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
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3
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
X757770119Page 19
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THIS MARGIN
9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
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1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
X757770123Page 23
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
X757770125Page 25
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
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1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
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Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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X757770116Page 16
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8 (continued)
(b) In an experiment to investigate the nature of particles individual electrons were fired one at a time from an electron gun through a narrow double slit The position where each electron struck the detector was recorded and displayed on a computer screen
The experiment continued until a clear pattern emerged on the screen as shown in Figure 8
The momentum of each electron at the double slit is 6middot5 times 10minus24 kg m sminus1
electron gun
electron
double slit
detector
computer screen
not to scaleFigure 8
(i) The experimenter had three different double slits with slit separations 0middot1 mm 0middot1 μm and 0middot1 nm
State which double slit was used to produce the image on the screen
You must justify your answer by calculation of the de Broglie wavelength
Space for working and answer
4
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THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
3
3
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
X757770119Page 19
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THIS MARGIN
9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
[Turn over
1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
X757770123Page 23
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
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THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
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THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
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Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
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X757770117Page 17
MARKS DO NOT WRITE IN
THIS MARGIN 8 (b) (continued)
(ii) The uncertainty in the momentum of an electron at the double slit is 6middot5 times 10minus26 kg m sminus1
Calculate the minimum absolute uncertainty in the position of the electron
Space for working and answer
(iii) Explain fully how the experimental result shown in Figure 8 can be interpreted
[Turn over
3
3
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
X757770119Page 19
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THIS MARGIN
9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
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THIS MARGIN
9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
X757770121Page 21
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THIS MARGIN
10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
[Turn over
1
2
X757770122Page 22
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THIS MARGIN
10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
X757770123Page 23
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
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THIS MARGIN
11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
X757770125Page 25
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THIS MARGIN
11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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THIS MARGIN
12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
X757770127Page 27
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
MARKS DO NOT WRITE IN
THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
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THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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X757770118Page 18
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9 A particle with charge q and mass m is travelling with constant speed v The particle enters a uniform magnetic field at 90deg and is forced to move in a circle of radius r as shown in Figure 9
The magnetic induction of the field is B
magnetic pole
magnetic pole
path of chargedparticle
Figure 9
magneticfield lines
(a) Show that the radius of the circular path of the particle is given by
mvrBq
= 2
X757770119Page 19
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THIS MARGIN
9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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THIS MARGIN
10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
[Turn over
1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
X757770123Page 23
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
X757770125Page 25
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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THIS MARGIN
12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
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Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
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X757770119Page 19
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9 (continued)
(b) In an experimental nuclear reactor charged particles are contained in a magnetic field One such particle is a deuteron consisting of one proton and one neutron
The kinetic energy of each deuteron is 1middot50 MeV
The mass of the deuteron is 3middot34 times 10minus27 kg
Relativistic effects can be ignored
(i) Calculate the speed of the deuteron
Space for working and answer
(ii) Calculate the magnetic induction required to keep the deuteron moving in a circular path of radius 2middot50 m
Space for working and answer
[Turn over
4
2
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
[Turn over
1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
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11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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THIS MARGIN
12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
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2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
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THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
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THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
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Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
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X757770120Page 20
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9 (b) (continued)
(iii) Deuterons are fused together in the reactor to produce isotopes of helium
32He nuclei each comprising 2 protons and 1 neutron are present in the reactor
A 32He nucleus also moves in a circular path in the same magnetic field
The 32He nucleus moves at the same speed as the deuteron
State whether the radius of the circular path of the 32He nucleus is greater than equal to or less than 2middot50 m
You must justify your answer 2
X757770121Page 21
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THIS MARGIN
10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
[Turn over
1
2
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
X757770123Page 23
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
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THIS MARGIN
11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
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THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
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Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770121Page 21
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10 (a) (i) State what is meant by simple harmonic motion
(ii) The displacement of an oscillating object can be described by the expression
y = Acosωt
where the symbols have their usual meaning
Show that this expression is a solution to the equation
22
2 0d y ω ydt
+ =
[Turn over
1
2
X757770122Page 22
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THIS MARGIN
10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
X757770123Page 23
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
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THIS MARGIN
11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
X757770125Page 25
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THIS MARGIN
11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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THIS MARGIN
12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
X757770128Page 28
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
MARKS DO NOT WRITE IN
THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
MARKS DO NOT WRITE IN
THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
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THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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X757770122Page 22
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10 (continued)
(b) A mass of 1middot5 kg is suspended from a spring of negligible mass as shown in Figure 10 The mass is displaced downwards 0middot040 m from its equilibrium position
The mass is then released from this position and begins to oscillate The mass completes ten oscillations in a time of 12 s
Frictional forces can be considered to be negligible
15 kg
0040 m
Figure 10
(i) Show that the angular frequency ω of the mass is 5middot2 rad sminus1
Space for working and answer
(ii) Calculate the maximum velocity of the mass
Space for working and answer
3
3
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THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
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THIS MARGIN
11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
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11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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THIS MARGIN
12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
MARKS DO NOT WRITE IN
THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
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16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770123Page 23
MARKS DO NOT WRITE IN
THIS MARGIN
10 (b) (continued)
(iii) Determine the potential energy stored in the spring when the mass is at its maximum displacement
Space for working and answer
(c) The system is now modified so that a damping force acts on the oscillating mass
(i) Describe how this modification may be achieved
(ii) Using the axes below sketch a graph showing for the modified system how the displacement of the mass varies with time after release
Numerical values are not required on the axes
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
(An additional graph if required can be found on Page 41)
3
1
1
[Turn over
X757770124Page 24
MARKS DO NOT WRITE IN
THIS MARGIN
11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
X757770125Page 25
MARKS DO NOT WRITE IN
THIS MARGIN
11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
X757770126Page 26
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THIS MARGIN
12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
X757770127Page 27
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12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
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THIS MARGIN
13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
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THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
MARKS DO NOT WRITE IN
THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
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THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770124Page 24
MARKS DO NOT WRITE IN
THIS MARGIN
11
foghorn
A ship emits a blast of sound from its foghorn The sound wave is described by the equation
( )sin ndash0 250 2 118 0 357y π t xsdot sdot=
where the symbols have their usual meaning
(a) Determine the speed of the sound wave
Space for working and answer
4
X757770125Page 25
MARKS DO NOT WRITE IN
THIS MARGIN
11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
X757770126Page 26
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THIS MARGIN
12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
X757770127Page 27
MARKS DO NOT WRITE IN
THIS MARGIN
12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
X757770128Page 28
MARKS DO NOT WRITE IN
THIS MARGIN
13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
MARKS DO NOT WRITE IN
THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
MARKS DO NOT WRITE IN
THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
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THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
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THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770125Page 25
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THIS MARGIN
11 (continued)
(b) The sound from the shiprsquos foghorn reflects from a cliff When it reaches the ship this reflected sound has half the energy of the original sound
Write an equation describing the reflected sound wave at this point
[Turn over
4
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THIS MARGIN
12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
X757770127Page 27
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THIS MARGIN
12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
X757770128Page 28
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13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
MARKS DO NOT WRITE IN
THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
MARKS DO NOT WRITE IN
THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
MARKS DO NOT WRITE IN
THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
MARKS DO NOT WRITE IN
THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770126Page 26
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THIS MARGIN
12 Some early 3D video cameras recorded two separate images at the same time to create two almost identical movies
Cinemas showed 3D films by projecting these two images simultaneously onto the same screen using two projectors Each projector had a polarising filter through which the light passed as shown in Figure 12
polarising filters
to cinema screen
film projectors
Figure 12
(a) Describe how the transmission axes of the two polarising filters should be arranged so that the two images on the screen do not interfere with each other
(b) A student watches a 3D movie using a pair of glasses which contains two polarising filters one for each eye
Explain how this arrangement enables a different image to be seen by each eye
1
2
X757770127Page 27
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THIS MARGIN
12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
X757770128Page 28
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THIS MARGIN
13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
MARKS DO NOT WRITE IN
THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
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THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
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THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
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THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
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THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770127Page 27
MARKS DO NOT WRITE IN
THIS MARGIN
12 (continued)
(c) Before the film starts the student looks at a ceiling lamp through one of the filters in the glasses While looking at the lamp the student then rotates the filter through 90deg
State what effect if any this rotation will have on the observed brightness of the lamp
Justify your answer
(d) During the film the student looks at the screen through only one of the filters in the glasses The student then rotates the filter through 90deg and does not observe any change in brightness
Explain this observation
[Turn over
2
1
X757770128Page 28
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THIS MARGIN
13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
MARKS DO NOT WRITE IN
THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
MARKS DO NOT WRITE IN
THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
MARKS DO NOT WRITE IN
THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
MARKS DO NOT WRITE IN
THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770128Page 28
MARKS DO NOT WRITE IN
THIS MARGIN
13 (a) Q1 is a point charge of +12 nC Point Y is 0middot30 m from Q1 as shown in Figure 13A
030 m
Y+12 nCQ1
Figure 13A
Show that the electrical potential at point Y is +360 V
Space for working and answer
(b) A second point charge Q2 is placed at a distance of 0middot40 m from point Y as shown in Figure 13B The electrical potential at point Y is now zero
Q2
030 m 040 m
Y+12 nCQ1
Figure 13B
(i) Determine the charge of Q2
Space for working and answer
2
3
X757770129Page 29
MARKS DO NOT WRITE IN
THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
MARKS DO NOT WRITE IN
THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
MARKS DO NOT WRITE IN
THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
MARKS DO NOT WRITE IN
THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770129Page 29
MARKS DO NOT WRITE IN
THIS MARGIN 13 (b) (continued)
(ii) Determine the electric field strength at point Y
Space for working and answer
(iii) On Figure 13C sketch the electric field pattern for this system of charges
Q2Q1
Figure 13C
(An additional diagram if required can be found on Page 41)
[Turn over
4
2
X757770130Page 30
MARKS DO NOT WRITE IN
THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
MARKS DO NOT WRITE IN
THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
MARKS DO NOT WRITE IN
THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770130Page 30
MARKS DO NOT WRITE IN
THIS MARGIN 14 A student measures the magnetic induction at a distance r from a long
straight current carrying wire using the apparatus shown in Figure 14
wire
I
protective casing
magnetic sensormagnetic
induction meter
Figure 14
r
The following data are obtained
Distance from wire r = 0middot10 mMagnetic induction B = 5middot0 microT
(a) Use the data to calculate the current I in the wire
Space for working and answer
(b) The student estimates the following uncertainties in the measurements of B and r
Uncertainties in r Uncertainties in B
reading plusmn0middot002 m reading plusmn0middot1 microT
calibration plusmn0middot0005 m calibration plusmn1middot5 of reading
(i) Calculate the percentage uncertainty in the measurement of r
Space for working and answer
3
1
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
MARKS DO NOT WRITE IN
THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
MARKS DO NOT WRITE IN
THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770131Page 31
MARKS DO NOT WRITE IN
THIS MARGIN 14 (b) (continued)
(ii) Calculate the percentage uncertainty in the measurement of B
Space for working and answer
(iii) Calculate the absolute uncertainty in the value of the current in the wire
Space for working and answer
(c) The student measures distance r as shown in Figure 14 using a metre stick The smallest scale division on the metre stick is 1 mm
Suggest a reason why the studentrsquos estimate of the reading uncertainty in r is not plusmn0middot5 mm
[Turn over
3
2
1
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
MARKS DO NOT WRITE IN
THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
MARKS DO NOT WRITE IN
THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770132Page 32
15 A student constructs a simple air-insulated capacitor using two parallel metal plates each of area A separated by a distance d The plates are separated using small insulating spacers as shown in Figure 15A
metal plates
capacitance meter
d
air gap
insulating spacer
Figure 15A
The capacitance C of the capacitor is given by
0
AC εd
=
The student investigates how the capacitance depends on the separation of the plates The student uses a capacitance meter to measure the capacitance for different plate separations The plate separation is measured using a ruler
The results are used to plot the graph shown in Figure 15B
The area of each metal plate is 9middot0 times 10minus2 m2
90
80
70
60
50
40
30
20
10
00000 020 040 060
Figure 15B
y = 83x minus 020
C (times 10minus10 F)
(times 103 mminus1 )
080 100 1201d
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
MARKS DO NOT WRITE IN
THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
MARKS DO NOT WRITE IN
THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770133Page 33
MARKS DO NOT WRITE IN
THIS MARGIN 15 (continued)
(a) (i) Use information from the graph to determine a value for εo the permittivity of free space
Space for working and answer
(ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air
Space for working and answer
(b) The best fit line on the graph does not pass through the origin as theory predicts
Suggest a reason for this
[Turn over
3
3
1
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
MARKS DO NOT WRITE IN
THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
MARKS DO NOT WRITE IN
THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770134Page 34
[BLANK PAGE]
Do NoT wRiTE oN THiS PAGE
X757770135Page 35
MARKS DO NOT WRITE IN
THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
MARKS DO NOT WRITE IN
THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770135Page 35
MARKS DO NOT WRITE IN
THIS MARGIN
16 A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre
(a) In the first method the student measures the mass of the sphere to be 3middot8 kg and the radius to be 0middot053 m
Calculate the moment of inertia of the sphere
Space for working and answer
(b) In the second method the student uses conservation of energy to determine the moment of inertia of the sphere
The following equation describes the conservation of energy as the sphere rolls down the slope
2 21 12 2
mgh mv Iω= +
where the symbols have their usual meanings
The equation can be rearranged to give the following expression
222 1Igh vmr
⎛ ⎞= +⎜ ⎟⎝ ⎠
This expression is in the form of the equation of a straight line through the origin
y gradient x= times
[Turn over
3
X757770136Page 36
MARKS DO NOT WRITE IN
THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770136Page 36
MARKS DO NOT WRITE IN
THIS MARGIN
16 (b) (continued)
The student measures the height of the slope h The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16
data logger
not to scale
Figure 16
lightgate
height ofslope h
The following is an extract from the studentrsquos notebook
h (m) v (m sminus1) 2gh (m2 sminus2) v2 (m2 sminus2)
0middot020 0middot42 0middot39 0middot18
0middot040 0middot63 0middot78 0middot40
0middot060 0middot68 1middot18 0middot46
0middot080 0middot95 1middot57 0middot90
0middot100 1middot05 1middot96 1middot10
m = 3middot8 kg r = 0middot053 m
(i) On the square-ruled paper on Page 37 draw a graph that would allow the student to determine the moment of inertia of the sphere
(ii) Use the gradient of your line to determine the moment of inertia of the sphere
Space for working and answer
3
3
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770137Page 37
(An additional square-ruled paper if required can be found on Page 42)
[Turn over for next question
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770138Page 38
MARKS DO NOT WRITE IN
THIS MARGIN
16 (continued)
(c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method
Use your knowledge of experimental physics to comment on the studentrsquos statement
[END oF QUESTioN PAPER]
3
X757770139Page 39
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770139Page 39
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 2 (b) (ii)
r
Figure 2C
ω
Additional diagram for Question 5 (b) (i)
A B
spacecraftacceleratingin this direction
Figure 5A
X757770140Page 40
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Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
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X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770140Page 40
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 5 (b) (ii)
spacecraftmoving ata constantspeedA B
Figure 5B
Additional diagram for Question 7 (b) (ii)
0 500 1000 1500 2000λ (nm)
Inte
nsit
y
curve A
curve B
Figure 7
X757770141Page 41
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THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770141Page 41
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
Additional diagram for Question 10 (c) (ii)
time0
disp
lace
men
t fr
omeq
uilib
rium
pos
itio
n
Additional diagram for Question 13 (b) (iii)
Q2Q1
Figure 13C
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770142Page 42
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770143Page 43
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770144Page 44
MARKS DO NOT WRITE IN
THIS MARGINADDiTioNAL SPACE FoR ANSwERS AND RoUGH woRK
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X757770145Page 45
ACKNOWLEDGEMENT
Question 1 ndash Calvin Chanshutterstockcom
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
X7577711copy
NationalQualications2016 AH
X7577711 PhysicsRelationships Sheet
TUESDAY 24 MAY
900 AM ndash 1130 AM
AHTP
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 02
Relationships required for Physics Advanced Higher
dtdsv
a dvdt
d2sdt 2
v u at
s ut 12
at 2
v2 u2 2as
ddt
ddt
d2dt 2
o t
ot 12t 2
2 o2 2
s r
v r
at r
ar v 2
r r 2
F mv2
r mr 2
T Fr
T I
L mvr mr2
L I
EK 12
I 2
2rMm
GF
rGMV
rGMv 2
24 brightnessapparent
rLb
Power per unit area T4
L 4r2T4
rSchwarzschild2GM
c2
E hf
hp
mvr nh2
4 hpx x
4 htE
F qvB
2f
a d2ydt 2 2y
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 03
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
y Acost or y Asint
v (A2 y2)
EK 12
m 2(A2 y2)
EP 12
m 2y2
y Asin2( ft x
)
2x
2 1 0 where
21or differencepath optical
m
mm
x l2d
d
4n
x Dd
n tan iP
F Q1Q2
4or2
E Q
4or2
V Q
4or
F QE
V Ed
F IlBsin
B oI2r
c 1oo
t RC
XC VI
XC 1
2fC
L dIdt
E 12
LI2
XL VI
XL 2fL 222
ZZ
YY
XX
WW
222 ZYXW
=E k 2A
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 04
Vpeak 2Vrms
s v t
E mc2
Ipeak 2Irms
v u at hfE
Q It
s ut 12
at 2
EK hf hf0
V IR
v2 u2 2as
E2 E1 hf
P IV I2R V 2
R
s 12
u v t
T 1f
RT R1 R2
W mg
v f
1RT
1R1
1R2
F ma
dsin m
E V Ir
EW Fd
n sin1
sin2
V1 R1
R1 R2
VS
EP mgh
sin1
sin2
1
2
v1
v2
V1
V2
R1
R2
EK 12
mv2
sinc 1n
C QV
P Et
I kd2
E 12
QV 12
CV 2 12
Q2
C
p mv
I PA
Ft mvmu
2rMmGF
t t
1 vc
2
l l 1 vc
2
fo fsv
v vs
z observed rest
rest
z vc
v H0d
d v t
EW QV
path difference m or m 12
where m 0 1 2
random uncertainty max value - min value
number of values
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 08
[BLANK PAGE]
DO NOT WRITE ON THIS PAGE
Page 058
Additional Relationships
Circle Table of standard derivatives
Table of standard integrals
circumference = 2πr
area = πr2
Sphere
Trigonometry
Moment of inertia
area = 4πr2
volume = πr3
point mass
I = mr2
rod about centre
I = ml2
rod about end
I = ml2
disc about centre
I = mr2
sphere about centre
I = mr2
f (x) f (x)
sinax acosax
cosax ndash asinax
f (x) f (x)dx
sinax cosax + C
cosax sinax + C
1a
1a
43
θ
θ
θ
θ θ
=
=
=
+ =2 2
sin
cos
tan
sin cos 1
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
112
13
12
25
int
Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
Page 07
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Page 08
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Page 06
1 H 1
Hyd
roge
n
3 Li
21
Lit
hium
4 Be
22
Ber
ylliu
m
11 Na
28
1
Sodi
um
12 Mg
28
2
Mag
nesi
um
19 K2
88
1
Pot
assi
um
20 Ca
28
82
Cal
cium
37 Rb
28
188
1
Rub
idiu
m
38 Sr2
818
82
Stro
ntiu
m
55 Cs
28
181
88
1C
aesi
um
56 Ba
28
181
88
2B
ariu
m
87 Fr
28
183
218
81
Fra
nciu
m
88 Ra
28
183
218
82
Rad
ium
21 Sc2
89
2
Scan
dium
22 Ti
28
102
Tit
aniu
m
39 Y2
818
92
Ytt
rium
40 Zr
28
181
02
Zir
coni
um
57 La
28
181
89
2L
anth
anum
72 Hf
28
183
210
2H
afni
um
89 Ac
28
183
218
92
Act
iniu
m
104
Rf
28
183
232
10
2R
uthe
rfor
dium
23 V2
811
2
Van
adiu
m
41 Nb
28
181
21
Nio
bium
73 Ta2
818
32
112
Tant
alum
105
Db
28
183
232
11
2D
ubni
um
24 Cr
28
131
Chr
omiu
m
42 Mo
28
181
31
Mol
ybde
num
74 W2
818
32
122
Tung
sten
106
Sg2
818
32
321
22
Seab
orgi
um
25 Mn
28
132
Man
gane
se
43 Tc
28
181
32
Tech
neti
um
75 Re
28
183
213
2R
heni
um
107
Bh
28
183
232
13
2B
ohri
um
26 Fe
28
142
Iron 44 Ru
28
181
51
Rut
heni
um
76 Os
28
183
214
2O
smiu
m
108
Hs
28
183
232
14
2H
assi
um
27 Co
28
152
Cob
alt
45 Rh
28
181
61
Rho
dium
77 Ir2
818
32
152
Irid
ium
109
Mt
28
183
232
15
2M
eitn
eriu
m
28 Ni
28
162
Nic
kel
46 Pd
28
181
80
Pal
ladi
um
78 Pt
28
183
217
1P
lati
num
29 Cu
28
181
Cop
per
47 Ag
28
181
81
Silv
er
79 Au
28
183
218
1G
old
30 Zn
28
182
Zin
c
48 Cd
28
181
82
Cad
miu
m
80 Hg
28
183
218
2M
ercu
ry
5 B 23
Bor
on
13 Al
28
3
Alu
min
ium
31 Ga
28
183
Gal
lium
49 In2
818
18
3
Indi
um
81 Tl
28
183
218
3T
halli
um
6 C 24
Car
bon
14 Si 28
4
Silic
on
32 Ge
28
184
Ger
man
ium
50 Sn2
818
18
4
Tin 82 Pb
28
183
218
4L
ead
7 N 25
Nit
roge
n
15 P2
85
Pho
spho
rus
33 As
28
185
Ars
enic
51 Sb2
818
18
5
Ant
imon
y
83 Bi
28
183
218
5B
ism
uth
8 O 26
Oxy
gen
16 S2
86
Sulp
hur
34 Se2
818
6
Sele
nium
52 Te2
818
18
6
Tellu
rium
84 Po
28
183
218
6P
olon
ium
9 F 27
Flu
orin
e
17 Cl
28
7
Chl
orin
e
35 Br
28
187
Bro
min
e
53 I2
818
18
7
Iodi
ne
85 At
28
183
218
7A
stat
ine
10 Ne
28
Neo
n
18 Ar
28
8
Arg
on
36 Kr
28
188
Kry
pton
54 Xe
28
181
88
Xen
on
86 Rn
28
183
218
8R
adon
2 He 2
Hel
ium
57 La
28
181
89
2L
anth
anum
58 Ce
28
182
08
2C
eriu
m
59 Pr
28
182
18
2Pr
aseo
dym
ium
60 Nd
28
182
28
2N
eody
miu
m
61 Pm
28
182
38
2P
rom
ethi
um
62 Sm2
818
24
82
Sam
ariu
m
63 Eu
28
182
58
2E
urop
ium
64 Gd
28
182
59
2G
adol
iniu
m
65 Tb
28
182
78
2Te
rbiu
m
66 Dy
28
182
88
2D
yspr
osiu
m
67 Ho
28
182
98
2H
olm
ium
68 Er
28
183
08
2E
rbiu
m
69 Tm
28
183
18
2T
huliu
m
70 Yb
28
183
28
2Y
tter
bium
89 Ac
28
183
218
92
Act
iniu
m
90 Th
28
183
218
10
2T
hori
um
91 Pa
28
183
220
92
Pro
tact
iniu
m
92 U2
818
32
219
2U
rani
um
93 Np
28
183
222
92
Nep
tuni
um
94 Pu
28
183
224
82
Plu
toni
um
95 Am
28
183
225
82
Am
eric
ium
96 Cm
28
183
225
92
Cur
ium
97 Bk
28
183
227
82
Ber
keliu
m
98 Cf
28
183
228
82
Cal
ifor
nium
99 Es
28
183
229
82
Ein
stei
nium
100
Fm
28
183
230
82
Fer
miu
m
101
Md
28
183
231
82
Men
dele
vium
102
No
28
183
232
82
Nob
eliu
m
71 Lu
28
183
29
2L
utet
ium
103
Lr
28
183
232
92
Law
renc
ium
Ele
ctro
n A
rran
gem
ents
of E
lem
ents
Gro
up 1 (1)
Gro
up 2 (2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Gro
up 3 (13)
Gro
up 4 (14)
Gro
up 5 (15)
Gro
up 6 (16)
Gro
up 7 (17)
Gro
up 0 (18)
Tran
sitio
n E
lem
ents
Lant
hani
des
Act
inid
es
Ato
mic
num
ber
Sym
bol
Ele
ctro
n ar
rang
emen
t N
ame
Key
9
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