Cambridge A Level Physics 9702 — 2007 May/June Paper 4 · Variant 1

1 (a) Explain what is meant by a gravitational field. .......................................................................................................................................... ..................................................................................................................................... [1] (b) A spherical planet has mass M and radius R. The planet may be considered to have all its mass concentrated at its centre. A rocket is launched from the surface of the planet such that the rocket moves radially away from the planet. The rocket engines are stopped when the rocket is at a height R above the surface of the planet, as shown in Fig. 1.1. R 2R planet R Fig. 1.1 The mass of the rocket, after its engines have been stopped, is m. (i) Show that, for the rocket to travel from a height R to a height 2R above the planet’s surface, the change ΔEP in the magnitude of the gravitational potential energy of the rocket is given by the expression GMm ΔEP = . 6R [2] Examiner’s Use (ii) During the ascent from a height R to a height 2R, the speed of the rocket changes from 7600 m s–1 to 7320 m s–1. Show that, in SI units, the change ΔEK in the kinetic energy of the rocket is given by the expression ΔEK = (2.09 × 106)m. [1] (c) The planet has a radius of 3.40 × 106 m. (i) Use the expressions in (b) to determine a value for the mass M of the planet. M = …………………………… kg [2] (ii) State one assumption made in the determination in (i). .................................................................................................................................. ............................................................................................................................. [1]

Mark scheme: 1 (a) (region of space) where a mass experiences a force B1 [1] (b) (i) potential energy = (–)GMm / x C1 ∆EP = GMm/2R – GMm/3R M1 = GMm/6R A0 [2] (ii) EK = ½m (76002 – 73202) M1 = (2.09 × 106)m A0 [1] (c) (i) 2.09 × 106 = (6.67 × 10–11 M)/(6 × 3.4 × 106) C1 M = 6.39 × 1023 kg A1 [2] (ii) e.g. no energy dissipated due to friction with atmosphere/air rocket is outside atmosphere not influenced by another planet etc. B1 [1]

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2 (a) Use the kinetic theory of matter to explain why melting requires energy but there is no change in temperature. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [3] (b) Define specific latent heat of fusion. .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2] (c) A block of ice at 0 °C has a hollow in its top surface, as illustrated in Fig. 2.1. hollow ice Fig. 2.1 A mass of 160 g of water at 100 °C is poured into the hollow. The water has specific heat capacity 4.20 kJ kg–1 K–1. Some of the ice melts and the final mass of water in the hollow is 365 g. (i) Assuming no heat gain from the atmosphere, calculate a value, in kJ kg–1, for the specific latent heat of fusion of ice. specific latent heat = …………………………. kJ kg–1 [3] Examiner’s Use (ii) In practice, heat is gained from the atmosphere during the experiment. This means that your answer to (i) is not the correct value for the specific latent heat. State and explain whether your value in (i) is greater or smaller than the correct value. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................. [2]

Mark scheme: 2 (a) (on melting,) bonds between molecules are broken/weakened or molecules further apart/are able to slide over one another B1 kinetic energy unchanged so no temperature change B1 potential energy increased/changed so energy required B1 [3] (b) thermal energy/heat required to convert unit mass of solid to liquid M1 with no change in temperature/ at its normal boiling point A1 [2] (c) (i) thermal energy lost by water = 0.16 × 4.2 x 100 = 67.2 kJ C1 67.2 = 0.205 × L C1 L = 328 kJ kg–1 A1 [3] (ii) more energy (than calculated) melts ice M1 so, (calculated) L is lower than the accepted value A1 [2]

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3 Two charged points A and B are separated by a distance of 6.0 cm, as shown in Fig. 3.1. 6.0 cm A B d Fig. 3.1 The variation with distance d from A of the electric field strength E along the line AB is shown in Fig. 3.2. 20 E / kV m–1 15 10 5 0 0 2 4 6 d /cm position position of A of B Fig. 3.2 An electron is emitted with negligible speed from A and travels along AB. (a) State the relation between electric field strength E and potential V. .......................................................................................................................................... ..................................................................................................................................... [2] Examiner’s Use (b) The area below the line of the graph of Fig. 3.2 represents the potential difference between A and B. Use Fig. 3.2 to determine the potential difference between A and B. potential difference = …………………………. V [4] (c) Use your answer to (b) to calculate the speed of the electron as it reaches point B. speed = …………………………. m s–1 [2] (d) (i) Use Fig. 3.2 to determine the value of d at which the electron has maximum acceleration. d = …………………… cm [1] (ii) Without any further calculation, describe the variation with distance d of the acceleration of the electron. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................. [2]

Mark scheme: 3 (a) field strength = potential gradient M1 correct sign OR directions discussed A1 [2] (b) area is 21.2 cm2 ± 0.4 cm2 C2 (if outside ± 0.4 cm2 but within ± 0.8 cm2, allow 1 mark) 1.0 cm2 represents (1.0 × 10–2 × 2.5 × 103 =) 25 V C1 potential difference = 530 V A1 [4] (c) ½mv2 = qV ½ × 9.1 × 10–31 × v2 = 1.6 × 10–19 × 530 C1 v = 1.37 × 107 ms–1 A1 [2] (d) (i) d = 0 B1 [1] (ii) acceleration decreases then increases B1 some quantitative analysis (e.g. minimum at 4.0 cm) B1 [2] (any suggestion that acceleration becomes zero or that there is a deceleration scores 0/2) GCE A/AS LEVEL – May/June 2007 9702 04 √ √

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4 An ideal transformer has 5000 turns on its primary coil. It is to be used to convert a mains supply of 230 V r.m.s. to an alternating voltage having a peak value of 9.0 V. (a) Calculate the number of turns on the secondary coil. number = ……………………………… [3] (b) The output from the transformer is to be full-wave rectified. Fig. 4.1 shows part of the rectifier circuit. A R B Fig. 4.1 On Fig. 4.1, draw (i) diode symbols to complete the diagram of the rectifier such that terminal A of the resistor R is positive with respect to terminal B, [2] (ii) the symbol for a capacitor connected to provide smoothing of the potential difference across the resistor R. [1] Examiner’s Use (c) Fig. 4.2 shows the variation with time t of the smoothed potential difference V across the resistor R. V 0 0 t1 t2 t3 t4 t Fig. 4.2 (i) State the interval of time during which the capacitor is being charged from the transformer. from time ………… to time …………… [1] (ii) The resistance of the resistor R is doubled. On Fig. 4.2, sketch the variation with time t of the potential difference V across the resistor. [2]

Mark scheme: 4 (a) r.m.s. output = 9/√2 or peak input = 230√2 C1 NS/NP = VS/VP C1 NS = 138 → 140 turns A1 [3] (b) (i) four diodes correctly positioned regardless of output polarity M1 giving correct output polarity (all ‘point to left’) A1 [2] (ii) capacitor shown in parallel with R B1 [1] (c) (i) time t1 to time t2 B1 [1] (ii) sketch: same peak values M1 ripple reduced and reasonable shape A1 [2]

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5 (a) (i) Explain what is meant by a photon. .................................................................................................................................. ............................................................................................................................. [1] (ii) Show that the photon energy of light of wavelength 350 nm is 5.68 × 10–19 J. [1] (iii) State the value of the ratio energy of photon of light of wavelength 700 nm . energy of photon of light of wavelength 350 nm ratio = …………….. [1] (b) Two beams of monochromatic light have similar intensities. The light in one beam has wavelength 350 nm and the light in the other beam has wavelength 700 nm. The two beams are incident separately on three different metal surfaces. The work function of each of these surfaces is shown in Fig. 5.1. metal work function / eV tungsten 4.49 magnesium 3.68 potassium 2.26 Fig. 5.1 (i) Explain what is meant by the work function of the surface. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................. [2] Examiner’s Use (ii) State which combination, if any, of monochromatic light and metal surface could give rise to photo-electric emission. Give a quantitative explanation of your answer. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................. [3]

Mark scheme: 5 (a) (i) packet/discrete quantity/quantum (of energy) of e.m. radiation B1 [1] (ii) either E = (6.63 × 10–34 × 3 × 108)/(350 × 10–9) or E = (6.63 × 10–34 × 8.57 × 1014) M1 E = 5.68 × 10–19 J A0 [1] (iii) 0.5 B1 [1] (b) (i) energy of photon M1 to cause emission of electron from surface either with zero k.e or photon energy is minimum A1 [2] (ii) correct conversion eV → J or J → eV seen once B1 photon energy must be greater than work function C1 350 nm wavelength and potassium metal A1 [3]

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6 (a) Define the decay constant of a radioactive isotope. .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2] (b) Strontium-90 is a radioactive isotope having a half-life of 28.0 years. Strontium-90 has a density of 2.54 g cm–3. A sample of Strontium-90 has an activity of 6.4 × 109 Bq. Calculate (i) the decay constant λ, in s–1, of Strontium-90, λ = …………………………. s–1 [2] (ii) the mass of Strontium-90 in the sample, mass = …………………………. g [4] Examiner’s Use (iii) the volume of the sample. volume = …………………………. cm3 [1] (c) By reference to your answer in (b)(iii), suggest why dust that has been contaminated with Strontium-90 presents a serious health hazard. .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2]

Mark scheme: 6 (a) probability of decay M1 of a nucleus per unit time A1 [2] (allow 1 mark for A = λN, with symbols explained) (b) (i) λ = ln2/(28 × 365 × 24 × 3600) C1 = 7.85 × 10–10 s–1 A1 [2] (ii) A = (–)λN N = (6.4 × 109)/(7.85 × 10–10) C1 = 8.15 × 1018 C1 mass = (8.15 × 1018 × 90)/(6.02 × 1023) (e.c.f. for value of N) C1 = 1.22 × 10–3 g A1 [4] (iii) volume = (1.22 × 10–3/2.54 =) 4.8 × 10–4 cm3 A1 [1] (c) either very small volume of Strontium-90 has high activity or dust can be highly radioactive B1 breathing in dust presents health hazard B1 [2] GCE A/AS LEVEL – May/June 2007 9702 04

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7 A magnet is suspended vertically from a fixed point by means of a spring, as shown in Fig. 7.1. spring magnet R coil Fig. 7.1 One end of the magnet hangs inside a coil of wire. The coil is connected in series with a resistor R. (a) The magnet is displaced vertically a small distance D and then released. Fig. 7.2 shows the variation with time t of the vertical displacement d of the magnet from its equilibrium position. +D d 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 t /s –D Fig. 7.2 Examiner’s Use (i) State and explain, by reference to electromagnetic induction, the nature of the oscillations of the magnet. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................. [5] (ii) Calculate the angular frequency ω0 of the oscillations. ω0 = …………….……………… rad s–1 [2] (b) The resistance of the resistor R is increased. The magnet is again displaced a vertical distance D and released. On Fig. 7.2, sketch the variation with time t of the displacement d of the magnet. [2] Examiner’s Use (c) The resistor R in Fig. 7.1 is replaced by a variable-frequency signal generator of constant r.m.s. output voltage. The angular frequency ω of the generator is gradually increased from about 0.7ω0 to about 1.3ω0, where ω0 is the angular frequency calculated in (a)(ii). (i) On the axes of Fig. 7.3, sketch a graph to show the variation with ω of the amplitude A of the oscillations of the magnet. [2] A 0 0.7ω0 1.0ω0 1.3ω0 ω Fig. 7.3 (ii) State the name of the phenomenon illustrated in the graph of Fig. 7.3. ............................................................................................................................. [1] (iii) Briefly describe one situation where the phenomenon named in (ii) is useful and one situation where it should be avoided. useful: ....................................................................................................................... .................................................................................................................................. avoid: ........................................................................................................................ ............................................................................................................................. [2]

Mark scheme: 7 (a) (i) oscillations are damped/amplitude decreases B1 as magnet moves, flux is cut by coil B1 e.m.f./current is induced in the coil B1 causing energy loss in load OR force on magnet B1 energy is derived from oscillations of magnet OR force opposes motion of magnet B1 [5] (ii) T = 0.60 s C1 ω0 (= 2π/T) = 10.5 rad s–1 A1 [2] (b) sketch: sinusoidal wave with period unchanged or slightly smaller M1 same initial displacement, less damping A1 [2] (c) (i) sketch: general shape – peaked curve M1 peak at ω0 and amplitude never zero A1 [2] (ii) resonance B1 [1] (iii) useful: e.g. child on swing, microwave oven heating B1 avoid: e.g. vibrating panels, vibrating bridges B1 [2] (for credit, stated example must be put in context) Section B

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8 (a) State three characteristics of an ideal operational amplifier (op-amp). 1. ..................................................................................................................................... 2. ..................................................................................................................................... 3. ................................................................................................................................ [3] (b) An amplifier circuit for a microphone is shown in Fig. 8.1. – + 120 kΩ R V OUT X Fig. 8.1 (i) Name the type of feedback used with this op-amp. ............................................................................................................................. [1] (ii) The output potential difference VOUT is 5.8 V for a potential difference across the resistor R of 69 mV. Calculate 1. the gain of the amplifier circuit, gain = ……………………… [1] Examiner’s Use 2. the resistance of resistor X. resistance = ……………………… Ω [2] (iii) State one effect on the amplifier output of reducing the resistance of resistor X. .................................................................................................................................. ............................................................................................................................. [1]

Mark scheme: 8 (a) e.g. infinite (voltage) gain infinite input impedance zero output impedance infinite bandwidth infinite slew rate (any three, 1 each) B3 [3] (b) (i) negative (feedback) B1 [1] (ii) 1 gain (= 5.8/0.069) = 84 B1 [1] (ii) 2 gain = 1 + 120/X C1 84 = 1 + 120/X X = 1.45 kΩ A1 [2] (iii) gain increases OR bandwidth reduced OR output increases B1 [1] GCE A/AS LEVEL – May/June 2007 9702 04

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9 (a) Explain the principles behind the use of X-rays for imaging internal body structures. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [4] (b) Describe how the image produced during CT scanning differs from that produced by X-ray imaging. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [5]

Mark scheme: 9 (a) X-ray beam directed through body onto detector (plate) B1 different tissues absorb/attenuate beam by different amounts B1 giving ‘shadow’ image of structures B1 any other detail e.g. comment re sharpness or contrast B1 [4] (b) X-ray image is flat OR 2-dimensional (1) CT scan takes many images of a slice at different angles (1) these build up an image of a slice through the body (1) series of images of slices is made (1) so that 3D image can be built up (1) image can then be rotated (1) 1 mark for each point, max 5 B5 [5]

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10 An analogue signal is sampled at a frequency of 5.0 kHz. Each sample is converted into a four-bit number and transmitted as a digital signal. Fig. 10.1 shows part of the digital signal. START 0010 0101 1010 1111 0100 0010 0101 1010 1111 0100 most significant bit Fig. 10.1 The digital signal is transmitted and is finally converted into an analogue signal. (a) On the axes of Fig. 10.2, sketch a graph to show the variation with time t of this final analogue signal. 18 16 signal 14 12 10 8 6 4 2 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 t /ms [4] Fig. 10.2 (b) Suggest two ways in which the reproduction of the original analogue signal could be improved. 1. ..................................................................................................................................... .......................................................................................................................................... 2. ..................................................................................................................................... ..................................................................................................................................... [2]

Mark scheme: 10 (a) correct values of 2, 5, 10, 15 and 4 (–1 each error) B2 graph drawn as a series of steps M1 steps occurring at correct times A1 [4] (b) sample more frequently B1 greater number of bits B1 [2]

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11 (a) Fig. 11.1 is a block diagram showing part of a mobile phone handset used for sending a signal to a base station. aerial microphone Fig. 11.1 Complete Fig. 11.1 by labelling each of the blocks. [3] (b) Whilst making a call using a mobile phone fitted into a car, a motorist moves through several different cells. Explain how reception of signals to and from the mobile phone is maintained. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [4]

Mark scheme: 11 (a) modulator and oscillator identified B1 both amplifiers identified correctly B1 ADC and parallel-to serial converter identified B1 [3] (b) computer at cellular exchange B1 monitors signal strength B1 switches call from one base station to another B1 to maintain maximum signal strength B1 [4]

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