2011 AJC Prelim H2 Physics P2

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9646/02/AJC2011Prelim [Turn Over

2011 JC2 Preliminary Examination PHYSICS 9646/02 Higher 2 Paper 2 Structured Questions Monday 12 September 2011

1 hour 45 minutes

Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name and PDG in the spaces at the top of this page. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

For Examiner’s Use

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Deduction Total

ANDERSON JUNIOR COLLEGE

Candidate Name

PDG ( )

This document consists of 20 printed pages.

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9646/02/AJC2011Prelim

Data speed of light in free space, c = 3.00 x 108 m s-1 permeability of free space, μ0 = 4π x 10-7 H m-1 permittivity of free space, ε0 = 8.85 x 10-12 F m-1 (1/(36π)) x 10-9 F m-1 elementary charge, e = 1.60 x 10-19 C the Planck constant, h = 6.63 x 10-34 J s unified atomic mass constant, u = 1.66 x 10-27 kg

rest mass of electron, me = 9.11 x 10-31 kg rest mass of proton, mp = 1.67 x 10-27 kg molar gas constant, R = 8.31 J K-1 mol-1 the Avogadro constant, NA = 6.02 x 1023 mol-1 the Boltzmann constant, k = 1.38 x 10-23 J K-1 gravitational constant, G = 6.67 x 10-11 N m2 kg-2

acceleration of free fall, g = 9.81 m s-2

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Formulae

uniformly accelerated motion, 221 atuts +=

v2 = u2 + 2as work done on/by a gas, W = pΔV hydrostatic pressure, p = ρ g h

gravitational potential, r

Gm = -φ

displacement of particle in s.h.m., x = x0 sin ωt velocity of particle in s.h.m., v = v0 cos ωt

220 xxωv −±=

mean kinetic energy of a molecule of an ideal gas, resistors in series, R = R1 + R2 + … resistors in parallel, 1/R = 1/R1 + 1/R2 + …

electric potential, r4Q = V

0πε

alternating current/voltage, x = x0 sin ωt

transmission coefficient, T ∝ exp(-2kd)

where k = ( )2

28h

EUm −π

radioactive decay, x = x0exp(- λt)

decay constant, 21t

0.693 = λ

kTE2

3=

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1 (a) The variation with distance r of the gravitational field strength g of a mass is shown in Fig. 1.1.

Fig. 1.1 (i) Using values from Fig.1.1, plot a second graph using the axes drawn in Fig 1.2, to show

that g is inversely proportional to r 2.

Fig. 1.2

(ii) State how inverse proportion is demonstrated by your graph.

…………………………………………………………………………………..………………... ……………………………………………………………………………….…………………[1]

[2]

0 0

10.0 g / N kg-1

8.0

6.0

4.0

2.0

0 0 5.0 10.0 15.0 20.0 r / 106 m

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(b) Fig. 1.3 shows the variation with time t of the deceleration a of a body. The object comes to rest at the end of 4.0 s.

Fig. 1.3

On Fig. 1.4, draw a graph showing the variation with time of its velocity v.

Fig. 1.4 [3]

0 1.0 2.0 3.0 4.0 t / s

3.0

a / m s-2

2.0

1.0

0

0 1.0 2.0 3.0 4.0 t / s

v / m s-1

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(c) Measurements are made for the activity A of a radioactive sample over a period of time t. Fig.1.5 shows the variation with t of ln A.

Fig. 1.5 (i) Determine the gradient of the graph. Show your working.

gradient = ………………………………. [2] (ii) Suggest the relationship between A and t using Fig. 1.5 and your answer to (i).

…………………………………………………………………………………..………………... ……………………………………………………………………………….…………………..[2]

0 100 200 300 400 t / s

6.0

ln (A / Bq)

4.0

2.0

0

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2 Fig. 2.1 shows a student standing on a uniform plank that pivots on a log. The student intends to

cross a river. The plank has a mass of 25.0 kg and is 3.00 m long with a uniform cross-section. The log pivot is 0.50 m from the end of the plank. The student has a mass of 65.0 kg and stands at the end of the plank. A load is placed on the far end in order to balance the plank horizontally. The weight Wp of the plank and the force Fs exerted by the student on the plank are shown.

Fig 2.1

(a) On Fig. 2.1 draw and label two other forces acting on the plank. [1]

(b) Use the principle of moments to calculate the weight WL of the load needed on the right-hand end of the plank in order to balance the plank horizontally.

WL ..................................N [2]

(c) Explain why the load will eventually touch the ground as the student walks towards the

log. …………………………………………………………………………………..………………... ……………………………………………………………………………….……………………. …………………………………………………………………………………..………………... ……………………………………………………………………………….……………….….[2]

3.00 m

load

0.50 m

plank

ground ground river Fs Wp

log

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3 A glass tube of uniform cross-sectional area A is sealed at one end and contains some sand. The tube floats upright in water as shown in Fig. 3.1. The centre of mass of the tube and its contents is at C.

(a) The tube and its contents have a total mass M. The tube floats with a length L submerged in water. Show that the length L is given by the expression

waterofdensityisρwhere,AMLρ

=

[1]

(b) Sand is gradually removed from the tube. State what change, if any, occurs in the distance between the base of the tube and the centre of mass C of the tube and its contents. …………………………………………………………………………………..……………………... ……………………………………………………………………………….……………………….[1]

(c) The glass tube and its contents are replaced with a block of pure ice. State and explain qualitatively the change, if any, in the water level when the ice is melting. …………………………………………………………………………………..……………….......... …………………………………………………………………………………..……………….......... …………………………………………………………………………...……….……………………. ………………………………………………………………………………………..………………... …………………………………………………………………………………….………………….[3]

Fig. 3.1

L

sand

glasstube

water

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4 Three blocks of masses 4.0 g, 10.0 g and 3.0 g move on a frictionless horizontal track with speeds of 5.0 m s-1, 3.0 m s-1, and 4.0 m s-1 respectively as shown in Fig. 4.1. Velcro couplers make the blocks stick together after colliding.

Fig. 4.1 (a) Show that the final speed v of the train of three blocks after colliding is 2.24 m s-1.

[1] (b)

Fig. 4.2 shows the train of three blocks making a head-on collision with a sphere of mass 9.0 g which is initially at rest and suspended by a stiff light rod pivoted at C. After the collision, the train of three blocks moves off with 1

2v and the sphere swings upwards.

Fig. 4.2

(i) Find the speed of the sphere immediately after the train of three blocks collided with it.

speed = ………………………………m s-1 [2]

5.0 m s-1 3.0 m s-1 4.0 ms-1

4.0 g 10.0 g 3.0 g

θ

30.0 cm

9.0 g

v

train of three blocks

v 12

C

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(ii) The distance from the centre of the ball to point C is 30.0 cm. Calculate the angle θ subtended by the rod at the maximum height reached by the sphere after the collision.

θ = …………………….. ° [3] 5 (a) A boy blows gently across one end of a piece of glass tube. The air molecules in the tube will

then vibrate at the fundamental frequency.

(i) Draw on Fig. 5.1, arrows on the five dots to represent the amplitude and the direction of motion of the air molecules at a particular instant when a stationary wave has been set up along the tube. [2]

(ii) State the phase angle between the vibrations of air molecules along the tube situated at adjacent antinodes.

phase angle =…….……… rad [1]

(b) A two-source interference pattern is set up using monochromatic light of certain wavelength. The light passes through two slits a distance d apart, where d = 0.75 mm. A pattern of light is formed on a screen at a distance D = 2.8 m from the slits. The arrangement and the pattern seen on the screen are shown in Fig. 5.2. The lines shown are dark fringes. It is noticed that the maxima seen are not all of the same intensity.

The central bright fringe is located at O and the dark fringe at X is 5.88 mm from O.

Fig. 5.2

dark fringes

O

X

source

screen pattern (not to scale)

D

d

Fig. 5.1

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(i) On Fig. 5.3, sketch a graph of the intensity of light in the pattern seen.

[2] (ii) Calculate the wavelength of the light.

wavelength = ……………………………nm [2] (iii) Describe what happens to the fringes if both slits are covered with sheets of polaroid

and that in front of one of the slits is slowly rotated. …………………………………………………………………………………........................... …………………………………………………………………………………........................... …………………………………………………………………………………........................... ……………………………………………………………………………….………………….[2]

6 (a) A parallel beam of blue light of wavelength 4.0 × 10-7 m and intensity 500 W m-2 is incident

normally on a surface. Calculate (i) the energy of a photon of blue light,

energy = ………………………………. J [1]

O

intensity

position

Fig. 5.3

X

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(ii) the number of photons incident per second on 1.0 × 10-4 m2 of the surface.

number of photons arriving per second = ……………………… [2] (b) (i) State the de Broglie relation for the momentum p of a particle in terms of its associated

wavelength λ.

[1] (ii) Use the equation in (i) to calculate the momentum of a photon of blue light.

momentum = ……………………………… N s [1] (c) (i) Use your answers to (a)(ii) and (b)(ii) to calculate the change in momentum of photons

incident on 1.0 × 10-4 m2 of the surface in one second. Assume that the photons are absorbed by the surface.

change in momentum in 1 second = ………………… N [1] (ii) State and explain how your answer to (i) would change if the surface is instead

perfectly reflective. ………………………………………………………………………………..…………………… …………………………………………………………………………….…………………….[1]

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(iii) Suggest why your answer to (i) is referred to as a ‘radiation pressure’.

………………………………………………………………………………..…………………… …………………………………………………………………………….………………………. …………………………………………………………………………….…………………….[2]

7 Protons used as nuclear probes need to gain a significant amount of kinetic energy. This can be

achieved by accelerating the protons through an electric field. (a) In Fig.7.1, protons are accelerated when they pass between electrode 1 and 2 with a

potential difference of 2000 V.

Fig.7.2 is a sectional view of the space between the two electrodes in Fig.7.1 showing the

electric field lines.

Fig. 7.2

protons

Fig.7.1

1 2

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(i) State how Fig. 7.2 shows that the electric field at A is stronger than the field at B.

…………………………………………………………………………………………….........… …………………………………………………………………………………………………..[1]

(ii) State the potential at the point marked B, which is midway between the electrodes.

potential = ………………………………V [1]

(iii) Draw three equipotentials in the space between the two electrodes, passing through

the points marked A, B and C. [2] (b) A proton p is moving in the space between the two electrodes as shown in Fig.7.3. The

velocity of the proton p is indicated by the arrow

Fig.7.3 Draw an arrow on Fig. 7.3 at the position of proton p to show the force acting on it due to the electric field. [1]

(c) The energy that can be obtained with two electrodes is limited. Suggest and explain why

particles with energies of several GeV, as produced by modern accelerators, cannot be produced by two electrodes as above. …………………………………………………………………………………………….…….……….. .………………………………………………………………………………………….…...………….. ……………………………………………………………………………………………..…............ [2]

p

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(d) A linear accelerator (LINAC) overcomes the problem of producing high-energy particles without especially large potential difference by having a large number of accelerating stages. Fig. 7.4 shows a LINAC consisting of a large number n of accelerating stages achieved by passing the beam of protons through a series of n coaxial cylindrical tubes.

Fig. 7.4 Alternate tubes are connected to the same output terminal of a high frequency alternating p.d. The length of the gap between adjacent tubes is constant, but the length of the tubes increases along the accelerator path towards the target to ensure the alternating p.d. matches the position of the accelerating protons. For a proton to be continually accelerated, it is necessary that the potential difference between adjacent tubes reverse as the proton passes through. A proton travels at constant speed inside each tube. The proton crosses the gaps between the tubes at equal time intervals, and at each gap, their kinetic energy increases by a fixed amount.

(i) Explain why tube 2 must be at a more negative potential than tube 1 to accelerate the

protons leaving tube 1. ………………………………………………………………………………………..…………… ……………………………………………………………………………………………….… [1]

(ii) As the protons pass through tube 2, it is necessary that the potential of tube 2 changes

polarity. Explain why. …………………………………………………………………………………………………….. …….…………………………………………………………………………………………… [1]

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(iii) Calculate the number n of accelerating stages required to produce protons of kinetic energy 1.6 MeV with an applied alternating p.d. of amplitude 40 kV. The protons are accelerated when the p.d. is at the peak value. State any assumption made for your calculation.

n = ……………………………… [1] …………………………………………………………………………………………………….. ………………………………………………………………………………….……………… [1]

(e) The diagram of Fig. 7.5 shows the graph of energy against time for a proton moving down

part of the centre of the LINAC

.

Fig. 7.5

(i) Label with the letter P a point on the graph where the proton was midway between twoadjacent tubes. [1]

(ii) The acceleration is provided by a 40 kV, 10 MHz alternating source. Use this information

to add scales of energy and time to the axes of the graph. [2]

particle energy / KeV

time / μs 0

0

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(f) In Fig. 7.6, the graph of velocity against time for the protons has been added to the energy against time graph of Fig. 7.5.

.

Fig. 7.6 Comment on the velocity of the protons as they pass through a series of cylindrical tubes. …………………………………………………………………………………………….…….……….. .………………………………………………………………………………………….…...………….. ……………………………………………………………………………………………..…........... [2]

8 Many sensitive pieces of equipment such as computers and fax machines may be damaged by

current overload, even when this overload occurs for a relatively short time. One method of protection is to use a fuse in which the fuse wire melts a very short time after the circuit overloads. Typically this time is of the order of a few milliseconds. Fig 8.1 illustrates a one-ampere ‘quick-blow’ fuse. One way of measuring the time taken for the fuse wire to melt is to use a circuit containing a delay-trace oscilloscope. In this oscilloscope the trace remains visible on the screen for several seconds after the signal has been received.

energy

time / μs 0

0

velocity

Fig. 8.1

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Fig. 8.2 shows the screen of such an oscilloscope used in a circuit where a quick-blow fuse has been tested. Design an experiment using a delay-trace oscilloscope to measure the time taken for a 1 A fuse to blow in a circuit in which there is a current of 2 A. You should draw a circuit diagram showing how the equipment would be arranged. In your account you should pay particular attention to (a) the procedure to be followed, (b) the magnitudes of any potential differences and resistances used in your experiment, (c) how the oscilloscope would be used to measure the time taken for the fuse wire to melt, (d) the control of variables, (e) any precautions that you would take to improve the accuracy of the experiment.

Fig. 8.2

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Diagram ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ………………………………………………………………………………………………………………...

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………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. ………………………………………………………………………………………………………………... ……………………………………………………………………………………………………….……….. …………………………………………………………………………………………………………….[12]

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2011 AJC Prelim H2 Physics P2