TEMASEK JUNIOR COLLEGE2008 Preliminary ExaminationHigher 2

NAME CG

CENTRENUMBER

INDEX NUMBER

PHYSICSPaper 2 Structured Questions

Candidates answer on the Question Paper.No Additional Materials are required.

9745/0212 September 2008

1 hour 15 minutes

READ THESE INSTRUCTIONS FIRST

Write your name and C.G. on all the work you hand in.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 of each question or part question.

For Examiner’s Use

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This document consists of 14 printed pages.

[Turn over Data

speed of light in free space, c = 3.00 x 108 m s-1

permeability of free space, μo = 4π x 10-7 H m-1

permittivity of free space, εo = 8.85 x 10-12 Fm-1

(1 / (36 π)) x 10-9 Fm-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, s = ut + ½at2

v2 = u2 + 2as

work done on/by a gas, W = pΔV

hydrostatic pressure, p = ρgh

gravitational potential, =

displacement of particle in s.h.m. x = xo sin ωt

velocity of particle in s.h.m. v = vo cos ωt

=

resistors in series, R = R1 + R2 + …

resistors in parallel, 1/R = 1/R1 + 1/R2 + …

electric potential, V = Q / 4πεor

alternating current/voltage, x = xo sin ωt

transmission coefficient, T = exp(-2kd)

where k =

radioactive decay, x = xo exp (-λt)

decay constantλ =

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Answer all questions in the spaces provided.

1 The apparatus shown in Fig. 1.1 is set up to measure the speed of transverse waves on a stretched spring.

Fig. 1.1The following data are obtained.Distance between adjacent nodes = (0.150 ± 0.005) mFrequency of signal generator = (250 ± 10) Hz

(a) Calculate the speed of the transverse waves.

speed = m s-1 [2]

(b) Calculate the absolute uncertainty for the wave speed and hence express the wave speed with its absolute uncertainty to the appropriate number of significant figures.

speed = m s-1 [2]

(c) (i) In an attempt to reduce the absolute uncertainty, the frequency of the signalgenerator is increased to (500 ± 10) Hz. Explain why this will not result in a reduced absolute uncertainty.

[2]

(ii) State how the absolute uncertainty in the wave speed could be reduced.

[1]

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2 (a) (i) Define speed of an object.

(ii) Distinguish between speed and velocity.

[2]

(b) In Fig. 2.1, a rifle bullet is fired at an angle of 30o below the horizontal with an initial velocity of 800 m s-1 from the top of a cliff 100 m high.

(i) Calculate the time taken for the bullet to hit the ground below.

time taken = s [3]

(ii) Calculate the horizontal distance travelled by the bullet.

distance travelled = m [2]

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30o

800 m s-1

Fig. 2.1

cliff

3 This question brings together ideas about energy from different parts of the syllabus.

(a) A car is traveling along a horizontal road with constant speed. Energy is required to overcome the external forces opposing the motion of the car to maintain this constant speed. Suggest with a reason whether it would be worthwhile to develop a system whereby, when the car slows down, its kinetic energy would be re-stored for re-use when the car speeds up again.

[2]

(b) A glass U-tube containing liquid sodium is constructed from a hollow tubing having a square cross-section as shown in Fig. 3.1.

Electrodes are set into the upper and lower faces of the horizontal section and a current I is passed through the electrodes. A uniform horizontal magnetic field is applied at right angles to the axis of the horizontal section of the tube. A magnetic force is then exerted on the liquid due to the magnetic field.

This technique has been used as a means of pumping liquids. Explain why the energy required to maintain the current is larger when the liquid is in motion than when stationary.

[3]

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Fig. 3.1

I

magnetic fieldI

electrode

(c) A radioactive source emits ray -ray photons uniformly in all directions. In order to shield the source, it is placed at the centre of a hollow lead sphere as shown in Fig. 3.2.

It is found that the lead shield becomes hot after some time.

Explain this observation and suggest, with a reason, which region of the sphere is likely to experience the greatest heating effect.

[2]

4 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 a

horizontal distance x and released.

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

.

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

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source

lead shield

Fig 3.2

Fig. 4.1

harmonic motion.

[2]

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

The system is designed to reduce the oscillations of a building which has a natural frequency 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 transferred to the oscillator.

energy transferred = J [1]

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

amplitude = m [2]5 (a) A bar magnet with its axis along a coil axis, is released from rest at a position above

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Fig 4.2

the fixed coil so that it drops through the coil as shown in Fig. 5.1. The terminals of the coil are connected to a data logger which records the induced e.m.f. at regular intervals. The variation of the induced e.m.f. with time is shown in Fig. 5.2.

Fig. 5.1 Fig. 5.2

Explain, using the laws of electromagnetic induction, why

(i) two momentary deflections in opposite directions are observed,

[2]

(ii) the second momentary deflection is larger than the first.

[2]

(b) In Fig.5.3, the magnetic field has a uniform flux density of 2.0 x 10-4 T and is directed

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To data logger

Induced e.m.f.

time

out the paper. A wire coil placed at P is in the plane of the paper and away from the field. The coil has 200 turns, a total resistance of 2.0 and an area of 10 cm2.

The coil is moved from P to R in 0.20 s.

(i) Calculate the charge which flows in the coil.

charge= C [2]

(ii) Discuss whether there would be any effect on the charge flow for each of the following changes:

1. Increasing the number of turns in the coil.

[1]

2. Increasing the time to move it.

[1]

6 (a) Give two reasons why a 1 W laser may appear brighter than a 10 W filament lamp.

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PR

Fig.5.3

magnetic field

coil

[2]

(b) Draw and label the energy band diagram for an intrinsic semiconductor at room temperature, showing clearly how the bands might be filled.

[2]

(c) Use the band theory to explain why the addition of a small concentration of boron (Group III element) will decrease the resistivity of the semiconductor significantly.

[2]

7 Most man-made objects launched into space are satellites placed in a particular orbit around

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the Earth to function as TV transmitters, telephone relays or weather stations. Some spacecraft have been launched, however, to travel into much deeper space to explore the outer planets of our solar system. All spacecraft, whether satellites or deep space probes, must communicate with Earth by transmitting a radio signal.

The period and average orbital radius of two such satellites are given in the Fig. 8.2.

Satellite Period T /h Orbital radius R /km

A 1.63 7010

B 48.1 67100 Fig. 8.2

(a) (i) Satellite B has the larger orbital radius and the longer period. Using Newton’s law

of gravitation, derive the relationship between the orbital radius R and the period T.

[2]

(ii) Using the data from Fig. 8.2, calculate the orbital radius for a satellite with a period of 57.2 hours.

orbital radius = m [2]Most satellites in orbit around the Earth derive their power from a panel of solar cells which

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Fig. 8.1

solar panel

transmitter

Earth

convert sunlight into electrical power. One such telecommunications satellite transmits a continuous 360 W signal powered from its battery for 24 hours per day. The battery is recharged from a solar panel which has an efficiency of 16% while in direct sunlight of light intensity 1.5 kW m-2.

(b) (i) Calculate the minimum surface area of solar panel required to produce the 360 W for the transmitter.

surface area = m2 [2]

(ii) Give one reason why the surface area would have to be much greater than your answer in (b)(i).

[1]

For a spacecraft launched into the outer regions of the solar system, it is not practical to have its battery recharged by solar panels. Such spacecraft use a Radioisotope Thermoelectric Generator (RTG). This generator has no moving parts and contains two different metals joined to form a closed electric circuit. When the two junctions between these metals are kept at different temperatures, an electric current is produced. One junction is cooled by space while the other is heated by the decay from a radioactive isotope. RTGs are very reliable sources of power.

Nowadays, RTGs use plutonium-238 which is an alpha emitter with a half life of 88 years. Each alpha particle is emitted with a kinetic energy of 5.0 MeV.

(c) State one reason why solar panels are not practical in deep space, that is, far away from the solar system.

[1]

(d) Suppose such a spacecraft transmits for 120 minutes each day from a 12 V circuit which draws a current of 5.0 A while transmitting back to Earth. During the rest of the day, the transmitting circuit is shut down. The battery charging, however, carries on continuously.

(i) Show that the energy required per day for transmission is about 0.4 MJ.

[2](ii) The overall efficiency in the RTG battery charging system is 25%. Show that the

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steady power output required from the RTG is about 20 W.

[2]

(iii)

Calculate the minimum activity of the source (that is, the number of 5 MeV alpha particles emitted per second) required to generate the power.

activity = Bq [2]

(e) Show that the decay constant of Pu-238 is 2.5 x 10-10 s-1.

[2]

(f) Plutonium is one of the most dangerous chemical poisons known, as well as being a radioactive hazard. It has been estimated that 1 kg of this substance, suitably distributed would be enough to kill everyone on Earth. Comment on the risks involved in using plutonium as a fuel for spacecraft.

[2]

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