H2 2008 ALL JC Prelims Questions (2013)

7/23/2019 H2 2008 ALL JC Prelims Questions (2013)

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H2 Physics Revision (ALL JC 2008 Prelims) SAJC

1

All JC 2008 Prelims – Selected Questions

H2 Physics

Kinematics (Q1 – Q3)

HCI P2 Q11 A hot air balloon was rising steadily at a speed of 10.0 m s-1 when weather

conditions turned windy. A constant breeze of 3.0 m s-1 blew horizontally across

the sky, which caused the hot air balloon to travel with a resultant velocity of vR at

an angle to the horizontal, as shown in Fig. 1.1 below.

Fig. 1.1

(a) Calculate the magnitude of the resultant velocity vR . [2]

(b) A sandbag was dropped from the balloon. How far below the balloon would thesandbag be after 4.0 s, assuming that it had not landed on the ground?(Assume that the dropping of sandbags did not affect the velocity of the hot airballoon and that effects of air resistance on the sandbags were negligible.) [3]

(c) Another sandbag was dropped 2.0 s after the first. Considering only the verticalvelocities vy, sketch the vy vs. time t graph of the two sandbags from the time

the first sandbag was released to 3.0 s after the second sandbag was releasedon the axes below. Label your graphs clearly. Appropriate values should beindicated. [4]

(d) Using the graphs or otherwise, calculate the vertical distance of the secondsandbag above the first sandbag 3.0 s after the second sandbag was released.

[2]

vR

v / m

t / s




2

AJC P2 Q12 Fig. 1.1 shows the displacement-time graph of a moving object from a point P.

Fig. 1.1

(a) A student describes the motion of the object for time interval A to B as follows:

“T he object is moving away from point P. It is slowing down and is experiencingnegative acceleration towards P.”

Is the student’s description correct? Explain your reasoning. [4]

(b) Sketch the corresponding velocity-time graph of the object for the whole journey.[2]

TPJC P3 Q6(a)

3 (a) Two identical objects A and B slide down at the same time from an initialheight H from the ground along two frictionless slopes as shown below.

Fig. 6.1

dis lacement

A B C D Etime /s

A B C D Etime /s

velocit /m

H

θ θ

A B

H/2




3

(i) Write down an expression for the acceleration of object A as it slides down theslope, explaining your symbols. [1]

(ii) Sketch the velocity time graphs of A and B on the same axes. Label your graphsclearly. [3]

(iii) Explain whether the two objects will have the same speed at the bottom of theslope. [2]

(iv) Explain whether the two objects will reach the bottom of the slope at the sametime. [3]

Dynamics

AJC (H1) P2 Q6

4 (a) The floor of an elevator, mass 1800 kg, is at a distance 3.70 m above a springas shown in Fig. 4.1. It is at rest on the first floor when its cable snaps. A safetydevice clamps the elevator against guide rails so that a constant frictional force

of 4.40 kN opposes the elevator’s motion.

Fig. 4.1

(i) Show that the acceleration of the elevator is 7.37 m s-2. [1](ii) Calculate the speed of the elevator when it hits the spring. [2] (iii) Calculate the average power developed during this process before it hits the

spring. [2](iv) The spring is compressed by 0.9 m when the elevator comes to a rest. Using the

principle of conservation of energy, determine the force constant of the spring. Assume mass of spring is negligible. [2]

(v) The force constant found in (iv) is known to be accurate to 8%. How should theresult be presented? [1]

(b) Consider a woman of mass 60 kg, standing on a scale that reads in kilogram, inthe elevator when it is on the first floor as shown in Fig. 6.2. State the reading on

the scale after the cable snaps if the safety device fails to work. Explain youranswer. [3]

Fig. 4.2

spring

cable

elevatorguide rails

3.7 m

cable

elevator

scale




4

(c)(i) State the principle of conservation of momentum. [1]

(ii) A 0.25 kg skeet is fired at an angle of 30 to the horizontal with a speed of25 m s-1 as shown in Fig. 4.3. When it reaches the maximum height of 7.96 m, itis hit from below by a 15 g pellet traveling vertically upward at a speed of200 m s-1. The pellet is embedded in the skeet and they move together along

path A.

Fig. 4.3

1. Determine the velocity of the skeet at the maximum height of 7.96 m.[2]

2. Upon collision, skeet and pellet move off together with a velocity v at anangle to the horizontal. By applying (c)(i) to the skeet-pellet system in

the vertical direction, show that v sin = 11.321. [2]3. Determine the time of flight for the skeet-pellet system to complete path A.

[2]4. Suggest with a reason, whether the momentum of the skeet-pellet system

is conserved in the presence of air resistance. [2]

Forces (in Equilibrium)

MJC P3 Q5

5(a) Define moment of a force about a point. [2](b) A waiter holds a tray horizontally in one hand between fingers and thumb as

shown in Fig. 5.1.

Fig. 5.1.

P , Q and W are the three forces acting on the tray. W is the weight of the tray.

30

25 m s-1 200 m s-1 Path A7.96 m

skeet

pellet




5

(i) State two conditions that must be satisfied such that the tray will remainhorizontal and be in equilibrium. [2]

(ii) Given that the mass of the tray is 0.12 kg, calculate the magnitude of theforce P . [2]

(iii) Hence, calculate the magnitude of force Q. [2]

(c) The waiter places a glass on the tray. State and explain where the glass shouldbe positioned on the tray if the force P is to have the same value as thatcalculated in part (b)(ii). [2]

(d) (i) What is meant by the momentum of a body? [1]

(ii) A body, initially at rest, explodes into two unequal fragments of mass1

m

and2

m . Mass1

m has a velocity1v and mass

2m has a velocity

2v .

Using the principle of conservation of momentum, derive an expression

for 1

2

v

v . [2]

(iii) An isolated nucleus of mass25

4.0 x 10 kg

is initially at rest. It decays,emitting an alpha particle of mass

276.7 x 10 kg with kinetic energy of

141.2 x 10 J .

1. Find the speed of the alpha particle. [1]2. Hence, by considering the mass of the recoiling nucleus, use the

expression found in (d)(ii) or otherwise to find the speed of therecoiling nucleus. [3]

(e) Before the decay described in (d)(iii), the nucleus is situated at point P onFig. 5.2.

Fig. 5.2

For this question, we shall assume that the products of the decay will move off inthe horizontal path from the nucleus, indicated by the dotted line.

(i) Making use of the speed of the alpha particle deduced earlier, indicatewith a cross on Fig. 5.2, to full-scale, a possible position of the alpha

particle98.0 x 10 s

after the emission. [1]

(ii) Hence, indicate with an arrow, starting from P, the direction of movementof the recoiling nucleus. [1]

(iii) Estimate how far the recoiling nucleus would have moved in98.0 x 10 s

.

[1]

P




6

Work, Energy, Power

RJC P3 Q1(a)6 One end of a spring is attached to a rigid support and a mass is hung at the other

end. The mass oscillates about the equilibrium position B as shown in theFig. 6.1.

Ignoring the effects of air resistance, describe the energy changes from position A to B and from B to C. [3]

Circular Motion, Gravitation and Electric Field (Q7- 19)

AJC P2 Q7 7(a) A mass M is moving at 5.00 ms-1 along a horizontal frictionless guide which

bends into a vertical circle of radius r , as illustrated in Fig. 7.1.

Fig. 7.2 shows the velocity-time graph for the vertical component of the velocityalong the section ABC of the curve.

Unstretchedspring

Fig. 6.1

A

B

C

M A

B

C

r

Fig. 7.1




7

(i) With the aid of Fig. 7.2, find an appropriate value for the height of the vertical circle.Hence, find the value for the radius of the vertical circle, r . [3]

(ii)1.

Fig 7.3 shows the velocity-time graphs forthe horizontal component of the velocity

along the section ABC of the curve.

From Fig. 7.2 and Fig. 7.3, find thevertical and horizontal components of theacceleration of the mass M at B, 200 msafter it passes the point A. [3]

Fig. 7.2

Fig. 7.3




8

(ii)2.

(iii)

(iv)

(v)

Hence, find the resultant acceleration of the mass M at B.

Explain whether the magnitude of the resultant acceleration calculated in (bii) could have becalculated from the expression v2 / r, where v is the instantaneous speed of the mass M .

Without detailed mathematical calculation, deduce the total area between the curve and thetime axis of Fig. 7.3. Explain your answer.

With the aid of a labelled diagram showing all the forces acting on the mass M when it is atpoint C, deduce an expression for the minimum speed VC for the mass M to remain in contawith the track at point C in terms of r and g , where g is the acceleration of the free fall. Youmay assume that the density of air is negligible.

(b) Another mass 2M is moving at 5.00 ms-1 along the samehorizontal frictionless guide which bends into the samevertical circle of radius r , as illustrated in Fig. 7.4.

With reference to your answer in a(v) and the principle ofconservation of energy, explain whether the mass 2M isable to pass through point C and travels back to point A.[2]

8(a)AJC P3 Q1 The mass of the Earth is 5.98 x 1024 kg and the moon takes 27.4 days to orbit the EaShow that the distance between the centre of the Earth and the moon is 384 000 km.

(b) The orbit of the moon is actually elliptical and its distance from the Earth’s centre varies fr

356 000 km to 407 000 km. Find the maximum increase in kinetic energy of the moon acomes closer to the Earth. The mass of the moon is 7.36 x 10 22 kg.

maximum increase in kinetic energy = J

(c) Explain why the centre of the Earth is expected to lie on the plane of the moon’s orbit.

9(a)AJC P3 Q5

A man stands at the Earth’s equator. Due to the rotation of the Earth about its axis, and ta1 day = 8.6 x 104 s and radius of Earth = 6.4 x 106 m, find his

(i) angular velocity, [1](ii) his linear speed, [1]

(iii) his acceleration. [1]

(b) The man in (a) stands on a weighing scale. He finds that his weight shown on the scale isdifferent at the equator and at the North pole.

(i) Explain why there is a difference. [2]

(ii) State the location which shows his true weight. [1]

Fig. 7.42M A

C

r




9

(c) A particle rotates anticlockwise in a horizontal circle of radius 20 cm witha constant angular velocity of 3.5 rad s-1 as shown in Fig. 9.1.

The particle is at S at time zero and at P at time t . Q represents theprojection of point P onto the diameter through S. Measured with respect

to the origin O, the displacement and linear acceleration of Q in thedirection OS are y and a respectively.

(i) Describe the motion of Q. [1]

(ii) State the relationship between y and a. [1]

(iii) Sketch a labelled graph to show the variation of a with t .[3]

10

(a)

MJC P2 Q2 The following two equations may be used to find the gravitational potential energy, U ,

body of mass m:U = m g h ----- (1) and U = - G M m / r ------ (2)

State the condition(s) under which each of these equations may be used. [2

(b)(i) In a fictitious story by Jules Verne in 1865, three men were sent to space in a shell fired frogiant cannon from Florida.

Calculate the minimum speed needed for the shell to be projected vertically up to a heabove the surface of Earth that is equal to the Earth’s radius.

(Take radius of Earth to be 6.38 10 6 m and mass of Earth to be 5.97 10 24 kg)

(ii)

(ii)1.

Another shell is launched with the

escape speed , i.e., minimumspeed needed to escape theEarth’s gravitational field.

The following graph shows thevariation of the gravitationalpotential energy U with distancefrom the surface of Earth, x , of thisshell as it approaches infinity.

By considering the total energy ofthe shell at infinity, state the value

of total energy T , of this shell atany part of its path towards infinity.

T = ……………… J [1]

(ii)2. Hence, on the axis of Figure 2.1, sketch a graph to show how the kinetic energy K , of this svaries with the distance from the surface of the Earth. Label this graph clearly as K . [1]

O Q

P

y

Fig. 9.1

Energy

Distance from

surface of Earth

Gravitational

Potential Energy, U

Figure 2.1




10

(iii) When a spacecraft is launched into orbit, it is usually projected with a speed greater than Earth’s escape speed such that it will not be pulled back by gravity. However, the spin ofEarth can also give the spacecraft a ‘push’ such that it can remain in orbit.

Suggest a place on Earth where launching of the spacecraft is aided by the natural rotatio

Earth, and suggest the direction which the spacecraft should be launched in order to tadvantage of the Earth’s rotation. [1

11(a)

MJC P2 Q4 A charged particle q placed at point Ainside a uniform electric field betweentwo parallel plates with potential

difference of V is moved by anexternal force to point B via the pathshown in Figure 1. The plates areseparated by a distance d while the

distance of AB is x .

State and explain what the work doneon the charge would be from A to B. [2]

(b)

(i)

Figure 2 shows the path taken by anegative charge q when it is introducedwith a horizontal velocity u into a uniformE-field between two parallel plates. The

plates have a potential difference of V and are a distance d apart.

Explain why the expression F =1 2

2

04

QQ

r

cannot be used to calculate the forceexperienced by charge q in this case. [1]

(ii) Ignoring the effects of gravitational force, sketch, in Figure 2, the path of an alpha parwhich is projected with the same horizontal speed u . This alpha particle has the same amoof charge but twice the mass of the first particle q . Explain your answer. [3]

(iii) State how a magnetic field B should be directed, such that both particles mentioned will macross the plates un-deflected. [1]

12(a)(i)

NYJC P3 Q5 Prove that the expression for thegravitational potential difference between apoint P on the earth's surface and a distantpoint Q as shown below is

Rr

R-r GMVPQ

. [1]

A Bd

Figure 1

d qu

Figure 2

Earth

mass M

xP

rR




11

(ii) Show that if r is only slightly greater than R, the gravitational potential difference becomg(r-R) where g is the gravitational field strength on the earth's surface. [2]

(b) The graph on the next page shows how the gravitational potential difference between a pon the earth's surface and a distant point, distance x from the earth's surface, changes n

to the moon's surface. The moon's surface is 384 000 km from the earth's surface.

The gravitational potential difference is first increasing, then-achieving a maximum value finally decreasing to a smaller value on the moon's surface.

(i) Use the graph to determine the amount of potential energy converted as a mass of 200falls to the surface of the moon from a height of 14 000 km above the surface of the moonwhat speed will it hit the surface? [4]

(ii) What feature of the graph justifies the assumption that the potential energy of a bmeasured with respect to the moon's surface is proportional to its height above that surfaObtain from the graph the height to which this assumption is true. [3]

(iii) What is the value of the gravitational field strength at the point H where the gravitatiopotential difference is a maximum? Give a reason for your answer. [2]

(iv) Explain why the gravitational potential difference is a maximum at this point. [3]

(v) At what speed must a spacecraft be propelled from the surface of the moon if it is to rethe surface of the earth? [3]

13RJC P2 Q4 Two large plates with a potential difference V AB, are arranged in parallel as shown in Fig.

An electron is ejected with kinetic energy 1910.0 10 J from plate A and mov

perpendicularly towards plate B. It passes position X with 196.00 10 J of kinetic energy.

HGravitational

potentialdifference

/ MJ kg-1

62

61

60

59

58

330000 340000 350000 360000 370000 380000 x/




12

(a)

Calculate the distance d between plates Aand B, given that the electric field strengthbetween plate A and B is 50.0 N C-1. [2]

(b) Calculate the potential V0, at which the electron will stop momentarily and indicate tcorresponding equipotential line clearly on Fig 4. Show your working clearly. [4]

(c) Another electron of similar velocity is now ejected at an angle from plate A towards plate State whether the electron will stop before or after the equipotential line calculated in (b). [1

14RJC P3 Q2

The gravitational field strength at the surface of Planet X , of radius R , is 40 N kg-1. Fig. 2below shows three points A, B and C, and a scale showing their distances from the centre the planet.

Planet X

5R 5R 4R 4R 3R 3R 2R 2R R R 0

A B C

(a)(i) Show that the magnitude of the gravitational field strength at A is 1.6 N kg-1. [1]

(ii) Calculate the magnitude of the gravitational field strength at B. [1]

(b) Given that R is 2.0 x 107 m, and also given the field strengths in (a), determine anapproximate value for the magnitude of the gravitational potential difference

(i) between A and B, assuming that the gravitational field strength there to be the average vaof the field strengths at A and B; [2]

(ii) between A and C. [1]

(c) Planet X has approximately three times the radius of the Earth. Given that the gravitationafield strength at the surface of the Earth is 9.81 N kg -1, calculate the mass of Planet X in teof the mass, M , of the Earth. [3]

Fig. 2

A

d

electron

X

+10.0 VFig. 4




13

15

(a)

(b)

(c)

TJC P3 Q2 Fig. 3.1, which is not drawn to scale, shows how the electric potential V between two smalspherical charged conductors A and B varies along the line joining their centres. The distaD between the two conductors is very much larger than the radii of the conductors. At poinP, the electric potential is a maximum.

State the signs of the chargeof conductors A and B.Explain your answer. [2]

By considering the separatecontribution of A and B to theelectric potential, explain,with the aid of a diagram,why the graph has amaximum at point P. [3]

Use the asymmetry of the

curve to comment on therelative magnitude of thecharges on the twoconductors. Explain youranswer clearly. [3]

16(a)

(i)

(ii)

(iii)

TJC P3 Q6Figure 6.1 shows lines of equalgravitational potential near to thesurface of a small spherical asteroid

of mass M and radius R .

Explain why all the values ofpotential are negative. [2]

State the equation relating fieldstrength g and gravitationalpotential V at a point in thegravitational field. Hence, estimatethe value of g at the surface of theasteroid. [3]

Deduce the value of radius R andmass M of the asteroid. [5]

(iv) Calculate the escape speed from the surface of the asteroid. [2]

P x

V / V

BA

-80.0

-45.0

-5.0

Fig.

D

Surface of asteroid-5.0 x 105 J kg-1

-4.0 x 105 J kg-1

-2.6 x 105 J kg-1

-1.4 x 105

J kg-1

3.8 km

1.7 km

0.6 km

Fig. 6.1




14

(b)(i)

(ii)

Fig. 6.3 shows a man inside the space colony. Using thediagram provided, explain how the apparent weight of the manin such a space colony arises. [3]

A comfortable rotation rate for such a colony is 1.0 revolutionper minute. Determine the radius that this colony structure

should have in order to provide a simulated acceleration due to‘gravity’ of 9.81 m s-2. [3]

17

(a)

VJC P2 Q1 Two electrical charges, A and B, of 3.0 C and 2.0 Crespectively, are placed 10 m apart.

Find the distance between A and a point X, where the

resultant electric field strength due to A and B is zero. [3]

(b) Find the resultant electric potential at X due to A and B. [2]

(c) The answer in (b) is non-zero. From the definition of potential difference, this means that twork done to bring a unit charge from infinity to X is non-zero, even though the forces

experienced by the charge at the start and end of the process are zero. Explain why this is s

[2]

18 ACJC P2 Q2

In a hydrogen atom, an electron of mass me moves in a circular orbit of radius 0.53 10-10

about a fixed proton of mass mp = 1836 me. Assume g = 9.81 m s-2

.

(a) Find the magnitudes of(i) the gravitational force of the proton on the electron,(ii) the gravitational force of the Earth on the electron.

(iii) the electric force of the proton on the electron.

(b) Compare and comment on the magnitudes of the three forces found in (a) and (b) [2]

(c) With the help of your comments from (b) and your answers from (a), comment on centripetal force on the electron as it revolves in its circular orbit about the proton. [1]

10 m

3.0 CA

2.0

B

To centreof colon

Fig. 6.3




15

19(a)

CJC P3 Q1

The period T of the orbit around the Sun is given byGM

RT

3

2

where R is the radius of the orbit,G is the gravitational constant which has a unit of N kg-2 m2 andM is the mass of the Sun.

(i) Show that the equation is homogeneous in terms of base units. [2]

(ii) If the percentage uncertainties of T and M are ±3 % and ±4 % respectively, what will bepercentage uncertainty of R? [2]

(b) The Earth is 1.50 x 1011 m from the centre of the Sun and takes exactly one year to compone orbit. The planet Jupiter takes 11.9 years to complete an orbit of the Sun. Calculate thradius of Jupiter’s orbit. [2]

(c) “The gravitational force of the Earth on the moon causes it to rotate around the earth whilthe gravitational force of the moon on the earth is smaller so it will not affect the motion ofearth.” Comment on this statement. [2]

Thermal Physics (Q20 – Q22)

ACJC Prelims 200820 (a) One mole of hydrogen at a temperature of 420 K is mixed with one mole of

oxygen at 320 K. After a short period of time the mixture is in thermalequilibrium.

(i) Explain what happens as the two gases approach and then reachthermal equilibrium. [2]

(ii) The molecular kinetic theory leads to the derivation of the equation

2

3

1c Nm pV

Using the formula above and using the ideal gas equation, show that theaverage kinetic energy of the hydrogen molecules before they are mixed withthe oxygen molecules is 8.69 x 10-21 J where <c2> is the mean square speed.

[4]

(b) (i) Two different gases at the same temperature have molecules withdifferent mean square speeds. Explain why this is possible? [2]

(ii) Hence or otherwise, explain why in the earth’s atmosphere, there ishardly any hydrogen in the earth’s atmosphere, compared to oxygenmolecules. [2]




16

TJC Prelims 200821 (a) Suggest why the specific latent heat of vaporisation of water is much greater than the

specific latent heat of fusion of water. [2]

(b) Fig. 2.1 shows an insulated cylinder fitted with a perfectly fitting piston and a heater.

There is negligible friction between the cylinder and the piston. The cylinder contains afixed mass of an ideal gas.

The following two experiments are performed.

Experiment 1 The heater provides 150 J of energy with the piston fixed in position.The temperature rise of the gas is found to be 29 K.Experiment 2 The heater supplies 150 J of energy with the piston free to move sothat the gas expands at constant pressure. The temperature rise of the gas is now 18K.

(i) Using the first law of thermodynamics, explain why the temperature rise isdifferent in the two experiments. [2]

(ii) The change in internal energy of a gas is proportional to its change intemperature. Complete the table below to show the values of each of the

quantities U and W when the first law of thermodynamics is applied to the gas

in each experiment. Show your workings and state clearly whether each quantityis positive or negative.

U /J W/ J Q / J

Experiment 1 +150

Experiment 2 +150 [4]

ideal

gas

Fig. 2.1




17

IJC Prelims 200822 (a) State what is meant by

(i) an ideal gas, [1](ii) the state of a gas. [1]

(ii) Draw a graph in Fig. 1.1, to show the variation of pressure and volume asthe gas undergoes the processes A, B and C sequentially. Label theprocesses and indicate their directions clearly. [2]

Fig. 1.1

1. Calculate the heat supplied to the gas in process A. [2]

2. Calculate the work done on the gas in process B. [2]

3. For the entire cycle ABC, what is the change in the internal energyof the gas? [1]




18

Oscillations (Q23 – Q24)

AJC Prelim 200823

(ii) Given that k = 20.0 Nm-1, calculate for the system of cradle and baby

1. the period of the oscillation,

[1]2. the kinetic energy as it passes through the equilibrium position,

[1]3. the maximum net force experienced.

[1]

(iii) Sketch a labelled graph of the kinetic energy of the system againstdisplacement.

[2]

(iv) The baby’s father wants to take a picture of his child oscillating in thecradle.

Unknown to him, his camera exhibits a shutter delay of 3 s. If hedepresses the button when the cradle is at the highest point, how far isthe cradle away from its expected position in the picture?

[2]




19

TJC Prelims 200824 This question is about the oscillation of a mass between a pair of springs as shown in

Fig. 4.1.

(a) The system obeys Hooke’s Law with a stiffness constant k . The block is displaced ahorizontal distance x and released.

(i) Show that the initial acceleration a of the mass m is given by

m

kx a . [2]

(ii) Explain why the equation in (i) shows that the body will undergo simple harmonicmotion. [2]

(b) Such a system is used as a damper to reduce the movement of tall buildings inearthquakes or high winds as shown in Fig. 4.2.

The system is designed to reduce the oscillations of a building which has a naturalfrequency of 0.50 Hz. A sudden movement of the building displaces the block 0.70 m

from its equilibrium position relative to the building.

If the stiffness constant k of the system is 2.8 x 106 N m-1, find the energy transferredto the oscillator. [1]

(c) The oscillator is damped. It loses 50% of its energy on each oscillation. Find theamplitude of the oscillator after one complete oscillation. [2]

Fig. 4.1

Fig 4.2




20

Waves and Superposition (Q25 – Q31)

VJC Prelims 200825(a) A microwave transmitter emitting waves is placed facing a metal plate as shown

in the figure below.

A microwave detector is moved along the line PQ. A, B and C are threesuccessive points. When the detector is at A, the meter registers a maximumreading. As it is moved towards C, the meter reading decreases to a minimum atB and then increases again to a maximum at C.

(i) Explain why there is a variation in the meter’s readings at A, B and C.[3]

(ii) The distance between A and C is found to be 2.4 cm. Calculate thefrequency of the microwave being transmitted. [3]

(b) One such microwave transmitter is now mounted onto a spacecraft that hastraveled to the planet Saturn. It is transmitting with an output power of 25.0 W.

At the moment of transmitting the spacecraft is 1.32 x 1012 m from Earth.

(i) Assuming that the microwave transmitter is radiating uniformly in all

directions, calculate the power received on Earth by a dish aerial ofeffective area 180 m2. [3]

(ii) The actual power received by the dish aerial is 1.2 x 10-15 W. Suggestwhy the actual power received is greater than that calculated in (b)(i). [1]

CJC Prelims 2008 26 Sound travels by means of longitudinal waves in air and solids. A progressive sound wave of

wavelength and frequency f passes through a solid from left right.

In figure 3.1, the dots on line X represents the equilibrium positions of the atoms in the solid and don line Y represents the positions of the same atoms at a time t = to.

meter

Microwave

transmitter

PQ

A

B C

metal plate

detector




21

Excess pressure

displacement

D

line X

line Y

time = to

line Z

time = to+ T /4

Figure 3.1

Figure 3.2

Figure 3.3




22

(b) What does distance D in figure 3.1 represent? [1](c) Taking displacement to the right of equilibrium position as positive, sketch on

Fig 3.2, a graph of displacement against distance at time t o for Line Y. Label it Y. [2]

(d) Sketch on the same axis given on Fig. 3.2, a graph of displacement against position

of the atoms at time = t o + T/4, where T is the period of the wave. Label it Z. [1]

(e) Hence show on Fig. 3.1 on the line Z, the actual position of the particles at time = to + T/4.[2]

(f) Excess pressure is the difference between the pressure at a point above the atmosphericpressure. On figure 3.3, sketch the graph of excess pressure against distance at differentpositions at time to. [1]

(g) A person standing on the right side of line Y hears the sound at a frequency of f.Suppose he is moving to the left along the line Y at a constant speed, he will detect afrequency higher than f. Explain. [1]

RJC Prelims 200827 (b) Two coherent sources A and B, which are in phase with each other, emit microwave of

wavelength 40.0 mm. The amplitude of the wave from source B is twice that of source A. A detector is placed at the point P where it is 1.00 m from A and 1.18 m from B asshown in Fig. 7.2.

1.00 m

1.18 m

centre axis

A

B

O

P

Fig. 7.2

(i) Explain why the intensity detected at P is a minimum.[2]

(ii) Determine the ratio of the intensity at P to the intensity at O.

[3](iii) As the detector moved from P to O, a series of minima and maxima were

observed. Explain this phenomenon and state the total number of minimum and

maximum points that will be encountered along the way to O (inclusive of P andO).

[4]

(iv) State the type of interference at P when source B is changed to be 180°out-of-phase with source A.

[1]




23

NYJC Prelims 200828 (a) Explain what is meant by superposition in the context of waves. [2]

(b) Two microwave sources S1 and S2 are situated as shown below. The wavesemitted by the two sources are in phase and are polarized in the same plane.

A microwave detector is placed on a line XY which is parallel to and 3.2 mfrom the line joining S1 and S2. O lies on the perpendicular bisector of the line

joining S1 and S2. The detector produces an output which is proportional tothe displacement of the wave detected.

The detector is placed at P, a distance of 5.0 cm from O. The variation of theoutput of the detector with time with (a) only S1 switched on and (b) only S2 switched on are shown below.

(i) Using the figure above, determine the phase difference between thewaves at P. [1]

(ii) Calculate the wavelength of the microwaves. [3]

c = f

O

P

5.0 cm

X

Y

3.2 m

S1

S2

0.5 1.0 1.5 2.0

d e t e c t o r o u t p u t

t / 10-

s

S2 only

S1 only




24

(iii) The sources S1 and S2 are switched on together and as the detector ismoved from P towards X, the intensity of the microwave detectedfluctuates.

Assuming there are no maxima between O and P, deduce the distancefrom O to a point Q where the detector firsts encounters a maximum. [2]

(iv) The graph below shows how the intensity of the detected radiationvaries between O and Q when only S1 is switched on.

Using the same axes, sketch a graph to show how the intensity of thedetected microwave between O and Q varies when both S1 and S2 areswitched on. Label this graph (iv). [2]

(vi) Find the ratio of 1 / 2, where 1 is the intensity of the microwaves

detected at Q when S1 and S2 are polarized in the same plane and 2 is

that when S1 and S2 are polarized in perpendicular planes. [3]

(c) Microwaves such as those in (b) exert pressure on its detector.

(i) Explain why this is so. [3]

(ii) Deduce and explain the quantitative relationship between theamplitude of a microwave and the pressure it exerts. [2]

O Q

S1 only

Intensity / 10-3

W m-2

1.0




25

YJC Prelims 200829(c) Two radio aerials are separated by distance D along the ground. A sinusoidal

signal is emitted by an aircraft passing directly overhead, moving at speed v andheight h along a line PQR parallel to that between the aerials as shown in Fig.7.1. Point Q is equidistant from both aerials.

The signals received by the two aerials are added using an electronic device toproduce a resultant signal.

(i) If R, Q and P represent successive points along the aircraft path fromwhere the resultant signal received by the aerials are maxima, write downan expression for the possible path difference of the signal from R.

[1]

(ii) Hence explain why the intensity of the resultant signal fluctuates.[2]

(iii) Show that the frequency f of the occurrence of the maxima is given by the

relation f =vD

h where is the wavelength of the radio wave.

[2]

(iv) Calculate the period of these fluctuations when the speed and the altitudeof the aircraft are 80 m s -1 and 1500 m respectively, with an aerialseparation of 10 m and radio signal wavelength 3.0 cm.

[2]




26

IJC Prelims 200830 (a) (ii) Give an explanation for each of the following:

1. One can hear around corners, but not see around corners.[1]

2. Two flashlights held close together do not produceobservable interference pattern on a distant screen.

[1]




27

Current of Electricity, DC Circuits (Q32 – Q33)

TJC P3 Q4

31 A car battery has an e.m.f. of 12 V and an internal resistance of 0.50 . It is connected

to a parallel arrangement of four lamps, as shown in Fig. 4.1. Each lamp acts as apure resistor of constant resistance 30 . The total power dissipated in the lamps is16.9 W.

Fig. 4.1 (a) Calculate the effective resistance of the four lamps. [1]

(b) The owner of the car thinks that the brightness of the lamps can be increased byconnecting an additional resistor to the circuit so as to extract maximum powerfrom the battery. It is known that the maximum power which can be extractedfrom the battery is when the combined resistance of the four lamps and theadditional resistor is equal to the internal resistance of the battery.

State where the additional resistor should be connected so as to extract the

maximum power from the battery. [1]

(c) Calculate the resistance of the additional resistor. [2]

(d) With this resistor in the circuit, calculate the new total power dissipated in thefour lamps. [2]

(e) Comment on whether the car owner has achieved his aim. [1]

JJC P3 Q3

32 a) What do you understand by "internal resistance" of a battery? [1]

battery

12 V

0.50 .




28

(b) Fig 3.1 and 3.2 shows two circuits X and Y that are used by a student to test abattery of three identical cells. In circuit X there is no load resistor. In circuit Y aload resistor is connected. You can assume that the meters in the circuits areideal. Their readings are shown on each figure.

Fig. 3.1 Fig. 3.2

(i) Explain the difference between the voltmeter readings recorded in the two circuits.[1]

(ii) Calculate the internal resistance of a single cell. [2]

(iii)One of the cells in the battery is reversed. Determine the new reading

1. on the voltmeter in circuit X,

2. on the ammeter in circuit Y. [3]

(iv) The load resistor in circuit Y is replaced by an unknown device. The student findsthat the voltmeter reading decreases as the temperature of the device increases.Suggest what the device is. [1]

Electromagnetism (Q34 – Q35)

ACJCP2Q3 2008

33 (a) Define magnetic flux density and the tesla. [2]

(b) Sketch the magnetic flux patterns due to the following: [3]




29

(i) a long straight current carrying

wire

(ii) a flat circular current carrying coil

(c) A galvanometer has a square coil of sides 2.0 cm and consists of 40 turns ofwire. The coil is placed in two curved-poled magnets as shown below of fluxdensity 0.60 T so that for whatever positions of the coil, the magnetic field isalways parallel to the plane of the coil.

The coil with an attached pointer is held centrally between the curved-polemagnets. The coil moves in the annular space between the soft-iron core and the

magnet. A restraining torque, provided by the spiral springs placed above andbelow the coil is used to measure the current I flowing through the coil.

(i) When a current of 2.0 mA passes through the windings of the coil,determine the torque on the coil due to the magnetic force.

(ii) Suggest a reason why it is necessary for a radial field to be used to ensurethat the magnetic field is always parallel to the plane of the coil.

Currentgoing in

Currentcoming out

Currentgoing in




30

MJC P3 34

(a) Define the tesla. [1](b) A positively charged conductor is placed at a distance from a negative stationary

point charge as shown in Figure 2.1. Sketch the electric field pattern betweenthem. [2]

Figure 2.1 (c) A current I is now passed through the conductor from (b). The charge is made to

move towards the conductor with a speed of 1.5 cm s -1. It approaches theconductor at an angle of 30o as shown in Figure 2.2 below.The magnetic field strength due to the conductor varies with distance from the

conductor. At a perpendicular distance 20 cm away, its field strength is 20 mT.

Figure 2.2

(i) Given that the magnitude of the charge is – 3.0 C, calculate themagnitude of the force experienced by the charge due to the magneticfield of the wire when it is at a distance 20 cm away from the wire. [2]

(ii) Describe and explain how the charge will move initially due to the effect ofthis force. [2]

(d) In a separate experiment, another long conductor carrying current I is placedalongside a horizontal flat coil of rigid wire.

Figure 3.3

(i) Explain whether the resultant magnetic flux density at the centre of thecoil, P, is greater, smaller or unchanged when a current of the samemagnitude I flows through the coil, in a direction as shown in Figure 3.3.[2]

++

++

++

+

-

30o

1.5 cm s-1 I 20 cm

– 3.0 C -




31

EM Induction (Q36 –Q37)

ACJC P3 2008

35 (a) Define magnetic flux and explain what you understand by it.

(b) The diagram below shows a wire PQ of length l and a vertical conductingframe of negligible resistance placed in a uniform magnetic field B which isperpendicular to the plane of the frame. A light bulb of resistance R isconnected to the conducting frame. The wire falls vertically from rest andslides in contact with the sides of the conducting frame which has negligiblefriction.

(i) State and explain the direction of the induced current in wire PQ.

(ii) Show that current I flowing through the light bulb is given by the expression

Blv I

R

(iii) Hence, determine the expression for the magnetic force acting on wirePQ in terms of B, l , R and the velocity v of the wire PQ.

(iv) Given that the mass of rod PQ is 5.0 g, l = 60 cm, B = 0.50 T andR = 8.0 Ω, determine the terminal velocity of the rod.

X X X X X X X

X

X X X X X X XX

X X X X X X X

X

X X X X X X X

X

QP

Magnetic Field B R




32

VJC P2 Q2

36 A circular coil is placed with its axis vertical and a bar magnet, with its axis aligned with

the axis of the coil, is held above the coil and then dropped. A datalogger connected tothe coil records the e.m.f. induced in the coil at short time intervals and later draws agraph to show how the e.m.f. varies with time, as shown below.

(a) The diagram shows the graph of e.m.f. against time obtained as the magnet fallsthrough the coil.

Explain, using the laws of electromagnetic induction, the shape of the graph. [3]

(b) Give two arguments, one based on forces and one based on energy, to explain why

the magnet would take longer to fall if the datalogger were removed and, instead, theends of the coil were connected together.

(i) Based on forces: [2](ii) Based on energy: [2]

(c) Sketch on the copy of the graph, the graphs which would have been obtained if,separately (with the datalogger again connected)

To

dataloggercoil

magnet

S

0 100 200 300 400

-2.50

-1.25

0

1.252.50

e.m.f./V

t/ms




33

(i) the coil had been replaced with one with twice the number of turns [2]

(ii) the magnet had been dropped from about twice the height. [2]

Alternating CurrentsRJC P3 2008

37 (a) A hair blower used in Singapore is rated at 240 V r.m.s., 1000 W. A student plans to

bring the blower to the United States of America (USA), where the voltage is120 V r.m.s. .

(i) Explain why the current from the mains is alternating current rather than directcurrent. [2]

(ii) It was suggested that the student needs to bring a transformer along to USA in

order to operate the blower. Determine the transformer’s turns ratio s

p

N

N . [1]

(iii) Determine the r.m.s. current which the transformer will draw from the USA outlet

when the blower is operating at 1000 W. State any assumption you have madein your working. [3]

(b) Electricity is transmitted along the national grid using a combination of overhead andunderground cables. Suggest practical reasons why

(i) overhead cables are used outside cities. [1]

(ii) underground cables are used in cities. [1]

-

-

1.25

e.m.f./V

t/ms

0 100 200 300 400

-2.50

-1.25

0

1.25

2.50

e.m.f./V

t/ms




34

Quantum Physics (Q39 – Q43)

ACJC Prelim 08

38 (a) The Heisenberg position-momentum uncertainty principle can be stated asfollows:

where p and x are the uncertainty in the momentum and position.

An electron of kinetic energy 12.0 eV can be shown to have a speed of2.05 x 106 m s . Assume that such an electron is moving in the x-direction and

that the precision in measuring its speed is 0.50 %. { = h/2}

(i) Show that the minimum uncertainty with which you can simultaneouslymeasure the position of the electron along the x-axis due to Heisenberg’s

uncertainty principle is m10x5.65 -9 . [3]

ii) With reference to your answer to (a)(i) and the atomic diameter, comment onthe position of the electron if this is an orbital electron. [2]

(b) The scanning tunneling microscope (STM) is an electron microscope in which a

metal probe positioned at a distance d from a sample surface scans the surface.The surface is maintained at a potential difference of 6.0 V with respect to the tip.

Find the value of d at which the tip-surface transmission coefficient T is 0.0001. [2]




35

MJC Prelim 08 (part)

39

(a) To assess possible damage to the target surface, the target was placed under a

Scanning Tunnelling Microscope (STM).

(i) Briefing explain why tunneling is essential in the operation of an STM. [2]

(ii) A realistic scenario for the STM can be modelled as shown in a rough outlinedepicted in Figure 7.4 below:

Note that in Figure 7.4, V is the effective potential barrier height, and d is thebarrier width. Estimate the probability for an electron of energy 4.0 eV to tunnelthrough. [2]

(c) The mechanism for electron emission in the x-ray tube is that of thermionic emission,that is, emission due to heating. It is also possible for electrons to be emitted from ametallic surface by the process of photoelectric emission.

(i) Explain what is meant by photoelectric emission. [1]

d = 0.15 nm

V = 9.0 eV

electron

Figure 7.4




36

(ii) In a photoelectric experiment, a parallel beam of monochromatic radiation is

incident upon a metal surface of area 1.0 10-4 m2 in a vacuum tube. The metalhas a work function of 2.06 eV. The photocurrent against voltage graph is shownin Figure 3.5 below.

1. Calculate the maximum kinetic energy of the photoelectrons emitted. 1]2. Hence determine the frequency of radiation incident on the metal surface[2]

3. If one photoelectron is emitted for every 8000 photons incident on the metal,calculate the intensity of the radiation incident on the metal surface. [3]

TJC Prelim 0840 c An electron in an atom is considered to be in a potential well, as illustrated by the

sketch graph of Fig. 8.3.

(i) If the width of the potential well is about 1.0 x 10 -10 m, determine the minimumuncertainty in the momentum of the electron. [2]

I / μ A

V / V0-0.70

Figure 3.5

0.13

Energy

Distance fromcentre of atom

Energylevel ofelectronin atom

0

Fig. 8.3




37

CJC Prelim 08

41

The figure above represents a typical energy-level diagram (not to scale) for hydrogenatoms.

(d) An electron of energy 20.0 eV collides with a hydrogen atom in its ground state.The atom is excited to level 2 and the electron is scattered with a reduced velocity.The atom subsequently returns to its ground state with the emission of radiation.

Determine the velocity of the scattered electron. [3]

Energy/ eV

-0.54

-1.51

-3.40

434.0 nm

486.1 nm

656.3 nm

-13.601

2

3

45

P




38

Lasers & Semiconductors

MJC Prelim 08

42 Figure 6.1 illustrates the upper energy bands in two different classes of solid at absolute zero.The shaded areas represent occupied electron energy levels.

Figure 6.1

(a) State the classes of solids for X and Y.[2]

(b) At absolute zero, which solid, X or Y, will conduct electricity? Explain your choice usingband theory. [2]

(c) At higher temperatures, solid X can also conduct electricity. Explain, using band theory,

why this is so. [3]

Solid Y

Valenceband

Conductionband

Solid X

Conductionband

Valence

band

~ 2 eV




39

Nuclear Physics (Q45 – Q47)

CJC Prelim 08

43 (a) (i) State what is meant by the term nuclear binding energy . [1](ii) Figure 8.1 shows the variation of binding energy per nucleon number.

A uranium-235 nucleus undergoes fission and produces two fission products ofapproximately equal nucleon number. Using the data from Figure 8.1, estimate the energy released from the fission of one uranium-235 nucleus. [3]

(iii) One other possible reaction for uranium-235 is

n Kr BaU nU 1

0

90

36

144

56

236

92

1

0

235

92 2

The masses of particles are given below:

Mass of n1

0 = 1.009 u

Mass of U 235

92 = 235.124 u

Mass of Ba14456 = 143.923 u

Mass of Kr 90

36 = 89.920 u

Calculate the energy released by this reaction. [3]

(iv) Suggest, with a reason, which one of the two fission reactions of uranium-235 is morelikely to occur. [1]

Figure 8.1




40

(b) (i) Why is radioactive decay described as a “random process”? [1]

(ii) Describe how you would demonstrate that radioactive decay is a random process. [1]

(iii) Explain why it is not advisable for pregnant ladies to be exposed to a radioactive source.

(iv) Define decay constant. [1]

(c) The nuclide 9038Sr is a beta-emitter of half life 28 years but the nuclide 238

34 Pu emits twogroups of alpha-particles which differ in energy by 0.045 MeV.

(i) If a 9038Sr source emits many beta particles in one second today, estimate how long will it

take it to emit the same number of beta particles in the year 2064 A.D.? [4]

(ii) Express the energy difference in joules. [1]

(iii)Suggest how the energy is conserved in the two types of plutonium (Pu) disintegration,despite there being this difference in the energies of the alpha particles produced. [1]

MI Prelim 08

44(a) Fig. 6.1 below represents an experiment on Rutherford scattering in whichparticles are directed at a gold foil. The detector is shown in two positions in theevacuated chamber.

Fig. 6.1

(i) Why is it necessary to remove the air from the apparatus? [1]

(ii) Explain why the gold foil should be very thin. [1]

(iii) Explain why the count rate from the particle detector inposition 1 is much greater than that in position 2. [2]




41

VJC Prelim 08

45 Given

n2AgRhnU 1

0

113

y

x

45

1

0

235

92

and AHeHH4

2

3

1

2

1

(a) Find the number of protons and neutrons in the U235

92 nucleus. [2]

(b) Determine x, y and A in the two above nuclear reactions. [3]

(c) For each reaction, state whether energy is produced and give anexample of where they can occur. [3]

(d) Write down a similar equation for the fusion of two atoms of deuterium

( H2

1) to form helium of nucleon number 3. [3]

(e) In (d), given the mass of the deuterium nucleus is 2.015u, that of one of theisotopes of helium is 3.017u and that of the neutron is 1.009u, calculate theenergy released by the fusion of 1.0 kg of deuterium. Give your answer inelectron-volts. [6]

(f) If 30% of this energy were used in a nuclear power station to produce1.0 MW of electricity continuously, calculate the number of days that thestation would be able to function. [3]




42

Data Analysis

MJC Prelim

46 Ultrasonic sound waves (ultrasound) have frequencies outside the audible range of thehuman ear, that is, greater than about 20 kHz.

As ultrasound passes through a medium, wave energy is absorbed. The rate at whichenergy is absorbed by unit mass of the medium is known as dose-rate. The dose-rate ismeasured in W kg-1. The total energy absorbed by unit mass of the medium is knownas the absorbed dose. This is measured in J kg -1 or, as in this question, kJ kg -1.

Under certain circumstances, biological cells may be destroyed by ultrasound. The effecton a group of cells is measured in terms of the survival fraction (SF ),

SF = exposurebeforecellsof number

exposureafter survivingcellsof number .

For any particular absorbed dose, it is found that the survival fraction changes as thedose-rate increases.

Figure 1.1 shows the variation with dose-rate of the survival fraction for samples of cellsin a liquid. The absorbed dose for each sample of cells was 240 kJ kg -1.

Figure 1.1(a) (i) Read off from Figure 1.1 the survival fraction for a dose rate of 200 W kg-1. [1]

(ii) Calculate the exposure time for an absorbed dose of 240 kJ kg-1 and at adose-rate of 200 W kg-1. [2]

(b) Survival fraction depends not only on dose-rate but also on absorbed dose.

Figure 1.2 shows the variation with dose rate of )(log10 SF for different values of

absorbed dose.

survival

fraction

dose rate / W kg-1




43

Figure 1.1(i) Identify the line in Figure 1.2 that corresponds to the data given in Figure

1.1. Label this line L . [1]

(ii) Suggest a reason for plotting survival fraction on a logarithmic scale. [1]

(iii) By reference to Figure 1.2, complete the table of Figure 1.3 for adose-rate of 200 W kg-1.

Abso rbed dose / kJ kg-1 log10 (SF )

50

100

160

240

340

450

560

Figure 1.3[3]




44

(c) Use your values in the table of Figure 1.3 to plot, on the axes of Figure 1.4, a

graph to show the variation with absorbed dose of )(log10 SF for the dose rate of

200 W kg-1. [3]

Figure 1.4

(d) Theory suggests that at a dose-rate of 200 W kg -1, two separate effects may give

rise to cell destruction. According to this theory, one of the effects becomesapparent only at higher absorbed doses. What evidence is provided for thistheory by

(i) Figure 1.2 [1]

(ii) Figure 1.4? [2]

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0 100 200 300 400 500 600

absorbed dose / kJ kg-1

log10(SF)




45

(e) The theory outlined in (d) suggests that the resultant survival fraction (SF )R dueto the two independent effects which have survival fractions (SF )1 and (SF )2 isgiven by the expression

(SF)R = (SF)1 x (SF )2

(i) Give the corresponding expression of RSF )(log10 in terms of 110 )(log SF and

210 )(log SF . You may wish to use an equation of the form

)(log)(log)(log 101010 baab . [1]

(ii) State how the graph of Figure 1.4 may be used to determine RSF )( for an

absorbed dose of 560 kJ kg-1. [1]

(iii)Discuss whether it is possible, by reference to your graph of Figure 1.4, to

determine separate values of 1)(SF and 2)(SF for the absorbed dose of 560

kJ kg-1. [2]

N2007 H2 A Levels Paper 2 Question 7 (Data Analysis)

47 When some substances are in the solid state, they exist as positively-chargedand negatively-charged ions arranged in a cubic lattice, as illustrated in Fig. 7.1.

A starting point for the understanding of lattice energies is to consider thepotential energy E p, between two ions X and V.




46

Fig. 7.2 shows the variation with distance r between X and Y of E p.

(a) (i) The gradient G of the graph varies with the distance r. Show that, starting fromthe definition of work done, for any value of r the magnitude of the force Fbetween X and Y is given by the expression

F = G [2]

(ii) Suggest how Fig. 7.2 indicates that, for some values of r, the force between Xand V is attractive and, for other distances, the force is repulsive. [2]

(iii) Use Fig. 7.2 and the expression in (i) to determine the magnitude of theforce, in newton, for values of the distance equal to1. 2.8 x 10-10m, [1]

2. 5.0 x 10-10

m. [3]




(b) The variation with distance r of the potential energy E~ may be represented by theexpression

8r

B

r

A Ep

where A and B are constants.

By reference to Fig. 7.2, state two features of the force represented by the term

8r

B in this expression. [2]

(c) Fig. 7.3 shows part of Fig. 7.2, drawn on a larger scale.

Thermal energy of the ions causes them to vibrate. The ions have a total energyof - 6.0 eV.

(i) Use Fig. 7.3 to determine, for these ions,1. the values of r between which they vibrate, [2]2. the kinetic energy of the ions at distance r= 3.5 x 10-10 m. [2]

(ii) State why, although the ions are oscillating, their motion is not SHM. [1]

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H2 2008 ALL JC Prelims Questions (2013)