9702_s12_qp_43
A paper of Physics, 9702
Questions:
13
Year:
2012
Paper:
4
Variant:
3
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1
Define gravitational potential at a point. The gravitational potential φ at distance r from point mass M is given by the expression φ = – GM r where G is the gravitational constant. Explain the significance of the negative sign in this expression. A spherical planet may be assumed to be an isolated point mass with its mass concentrated at its centre. A small mass m is moving near to, and normal to, the surface of the planet. The mass moves away from the planet through a short distance h. State and explain why the change in gravitational potential energy ΔEP of the mass is given by the expression ΔEP = mgh where g is the acceleration of free fall. For Examiner’s Use The planet in has mass M and diameter 6.8 × 103 km. The product GM for this planet is 4.3 × 1013 N m2 kg–1. A rock, initially at rest a long distance from the planet, accelerates towards the planet. Assuming that the planet has negligible atmosphere, calculate the speed of the rock as it hits the surface of the planet. speed = m s–1
13. Gravitational fields  →  13.4. Gravitational potential
5. Work, energy and power  →  5.2. Gravitational potential energy and kinetic energy
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2
For Examiner’s Use The kinetic theory of gases is based on some simplifying assumptions. The molecules of the gas are assumed to behave as hard elastic identical spheres. State the assumption about ideal gas molecules based on the nature of their movement, their volume. For Examiner’s Use A cube of volume V contains N molecules of an ideal gas. Each molecule has a component cX of velocity normal to one side S of the cube, as shown in . cx side S The pressure p of the gas due to the component cX of velocity is given by the expression pV = NmcX where m is the mass of a molecule. Explain how the expression leads to the relation pV = 1 3Nm where is the mean square speed of the molecules. The molecules of an ideal gas have a root-mean-square (r.m.s.) speed of 520 m s–1 at a temperature of 27 °C. Calculate the r.m.s. speed of the molecules at a temperature of 100 °C. r.m.s. speed = m s–1
15. Ideal gases  →  15.3. Kinetic theory of gases
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3
For Examiner’s Use Define specific latent heat. The heater in an electric kettle has a power of 2.40 kW. When the water in the kettle is boiling at a steady rate, the mass of water evaporated in 2.0 minutes is 106 g. The specific latent heat of vaporisation of water is 2260 J g–1. Calculate the rate of loss of thermal energy to the surroundings of the kettle during the boiling process. rate of loss = W
14. Temperature  →  14.3. Specific heat capacity and specific latent heat
5. Work, energy and power  →  5.1. Energy conservation
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4
For Examiner’s Use A small metal ball is suspended from a fixed point by means of a string, as shown in . string ball x The ball is pulled a small distance to one side and then released. The variation with time t of the horizontal displacement x of the ball is shown in . x / cm – 6 – 4 – 2 0.2 0.4 0.6 0.8 1.0 t / s t / s The motion of the ball is simple harmonic. Use data from to determine the horizontal acceleration of the ball for a displacement x of 2.0 cm. acceleration = m s–2 For Examiner’s Use The maximum kinetic energy of the ball is EK. On the axes of , sketch a graph to show the variation with time t of the kinetic energy of the ball for the first 1.0 s of its motion. EK kinetic energy t / s 0.2 0.4 0.6 0.8 1.0
17. Oscillations  →  17.1. Simple harmonic oscillations
5. Work, energy and power  →  5.2. Gravitational potential energy and kinetic energy
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5
For Examiner’s Use Define electric field strength. An isolated metal sphere is to be used to store charge at high potential. The charge stored may be assumed to be a point charge at the centre of the sphere. The sphere has a radius of 25 cm. Electrical breakdown (a spark) occurs in the air surrounding the sphere when the electric field strength at the surface of the sphere exceeds 1.8 × 104 V cm–1. Show that the maximum charge that can be stored on the sphere is 12.5 μC. Calculate the potential of the sphere for this maximum charge. potential = V
18. Electric fields  →  18.3. Electric force between point charges
18. Electric fields  →  18.5. Electric potential
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6
For Examiner’s Use A sinusoidal alternating voltage supply is connected to a bridge rectifier consisting of four ideal diodes. The output of the rectifier is connected to a resistor R and a capacitor C as shown in . C R The function of C is to provide some smoothing to the potential difference across R. The variation with time t of the potential difference V across the resistor R is shown in . V / V t / ms Use to determine, for the alternating supply, the peak voltage, peak voltage = V the root-mean-square (r.m.s.) voltage, r.m.s. voltage = V For Examiner’s Use the frequency. Show your working. frequency = Hz The capacitor C has capacitance 5.0 μF. For a single discharge of the capacitor through the resistor R, use to determine the change in potential difference, change = V determine the change in charge on each plate of the capacitor, change = C show that the average current in the resistor is 1.1 × 10–3 A. For Examiner’s Use Use and the value of the current given in to estimate the resistance of resistor R. resistance = Ω
21. Alternating currents  →  21.1. Characteristics of alternating currents
21. Alternating currents  →  21.2. Rectification and smoothing
19. Capacitance  →  19.3. Discharging a capacitor
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7
For Examiner’s Use Two long straight parallel copper wires A and B are clamped vertically. The wires pass through holes in a horizontal sheet of card PQRS, as shown in . P Q S wire A wire B R There is a current in wire A in the direction shown on . On , draw four field lines in the plane PQRS to represent the magnetic field due to the current in wire A. A direct current is now passed through wire B in the same direction as that in wire A. The current in wire B is larger than the current in wire A. On , draw an arrow in the plane PQRS to show the direction of the force on wire B due to the magnetic field produced by the current in wire A. Wire A also experiences a force. State and explain which wire, if any, will experience the larger force. The direct currents in wires A and B are now replaced by sinusoidal alternating currents of equal peak values. The currents are in phase. Describe the variation, if any, of the force experienced by wire B.
20. Magnetic fields  →  20.4. Magnetic fields due to currents
20. Magnetic fields  →  20.5. Electromagnetic induction
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9
For Examiner’s Use State what is meant by the decay constant of a radioactive isotope. Show that the decay constant λ and the half-life t  of an isotope are related by the expression λt  = 0.693. In order to determine the half-life of a sample of a radioactive isotope, a student measures the count rate near to the sample, as illustrated in . detector to counter shielding sample of radioactive material For Examiner’s Use Initially, the measured count rate is 538 per minute. After a time of 8.0 hours, the measured count rate is 228 per minute. Use these data to estimate the half-life of the isotope. half-life = hours The accepted value of the half-life of the isotope in is 5.8 hours. The difference between this value for the half-life and that calculated in cannot be explained by reference to faulty equipment. Suggest two possible reasons for this difference. 1. 2.
23. Nuclear physics  →  23.2. Radioactive decay
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10
A student designs an electronic sensor that is to be used to switch on a lamp when the light intensity is low. Part of the circuit is shown in . +5 V + – 240 V sensing device output device processing unit –5 V X +5 V State the name of the component labelled X on . On , draw the symbols for two resistors to complete the circuit for the sensing device, a relay to complete the circuit for the processing unit. State the purpose of the relay. Suggest why the diode is connected to the output of the operational amplifier (op-amp) in the direction shown.
10. D.C. circuits  →  10.1. Practical circuits
10. D.C. circuits  →  10.3. Potential dividers
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11
For Examiner’s Use 11 High-speed electrons are incident on a metal target. The spectrum of the emitted X-ray radiation is shown in . intensity wavelength Explain why there is a continuous distribution of wavelengths, there is a sharp cut-off at short wavelength. State what is meant by the hardness of an X-ray beam, how hardness is controlled. For Examiner’s Use Suggest why, when producing an X-ray image, long-wavelength X-ray radiation poses a greater hazard to health than short-wavelength radiation. Suggest how this hazard is minimised.
24. Medical physics  →  24.2. Production and use of X-rays
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12
For Examiner’s Use 12 A person is to be investigated using a magnetic resonance (MR) scanner. This technique involves the use of two superimposed magnetic fields. Describe the functions of these two magnetic fields. The frequency f of the electromagnetic waves emitted by protons on relaxation in an MR scanner is given by the equation f = 2cB where B is the total magnetic flux density and c is a constant equal to 1.34 × 108 s–1 T–1. The magnetic flux density changes by 2.0 × 10–4 T for each 1.0 cm thickness of tissue in a section. The scanner is adjusted so that the thickness of each section is 3.0 mm. Calculate, for corresponding points in neighbouring sections, the difference in magnetic flux density, difference in flux density = T the change in emitted frequency. frequency change = Hz
20. Magnetic fields  →  20.5. Electromagnetic induction
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