Cambridge A Level Physics 9702 — 2010 May/June Paper 2 · Variant 3

1 A digital voltmeter with a three-digit display is used to measure the potential difference across a resistor. The manufacturers of the meter state that its accuracy is ±1% and ±1 digit. The reading on the voltmeter is 2.05 V. (a) For this reading, calculate, to the nearest digit, (i) a change of 1% in the voltmeter reading, change = ..............................................V [1] (ii) the maximum possible value of the potential difference across the resistor. maximum value = ..............................................V [1] (b) The reading on the voltmeter has high precision. State and explain why the reading may not be accurate. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2]

Mark scheme: 1 (a) (i) 1% of ±2.05 is ±0.02 A1 [1] (ii) max. value is 2.08 V A1 [1] (b) there may be a zero error/calibration error/systematic error M1 which makes all readings either higher or lower than true value A1 [2]

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2 (a) State the two conditions that must be satisfied for a body to be in equilibrium. For Examiner’s 1. ...................................................................................................................................... Use .......................................................................................................................................... 2. ...................................................................................................................................... .......................................................................................................................................... [2] (b) Three co-planar forces act on a body that is in equilibrium. (i) Describe how to draw a vector triangle to represent these forces. ........................................................................... ........................................................................... ........................................................................... ........................................................................... ........................................................................... ........................................................................... .......................................................................[3] (ii) State how the triangle confirms that the forces are in equilibrium. .................................................................................................................................. ..............................................................................................................................[1] (c) A weight of 7.0 N hangs vertically by two strings AB and AC, as shown in Fig. 2.1. For Examiner’s Use B C T1 35° T2 50° A 7.0 N Fig. 2.1 For the weight to be in equilibrium, the tension in string AB is T1 and in string AC it is T2. On Fig. 2.1, draw a vector triangle to determine the magnitudes of T1 and T2. T1 = ................................................... N T2 = ................................................... N [3] (d) By reference to Fig. 2.1, suggest why the weight could not be supported with the strings AB and AC both horizontal. .......................................................................................................................................... ......................................................................................................................................[2]

Mark scheme: 2 (a) no resultant force/sum of forces zero B1 no resultant moment/torque/sum of moments/torques zero B1 [2] (b) (i) each force is represented by the side of a triangle/by an arrow M1 in magnitude and direction A1 arrows joined, head to tail B1 [3] (could be shown on a sketch diagram) (ii) if the triangle is ‘closed’ (then the forces are in equilibrium) B1 [1] (c) triangle drawn with correct shape (incorrect arrows loses this mark) B1 T1 = 5.4 ± 0.2 N B1 T2 = 4.0 ± 0.2 N B1 [3] (d) forces in strings would be horizontal B1 (so) no vertical force to support the weight B1 [2]

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3 A cyclist is moving up a slope that has a constant gradient. The cyclist takes 8.0 s to climb For the slope. Examiner’s The variation with time t of the speed v of the cyclist is shown in Fig. 3.1. Use 8 v / m s–1 6 4 2 0 0 2 4 6 8 t / s Fig. 3.1 (a) Use Fig. 3.1 to determine the total distance moved up the slope. distance = ............................................. m [3] (b) The bicycle and cyclist have a combined mass of 92 kg. For The vertical height through which the cyclist moves is 1.3 m. Examiner’s Use (i) For the movement of the bicycle and cyclist between t = 0 and t = 8.0 s, 1. use Fig. 3.1 to calculate the change in kinetic energy, change = .............................................. J [2] 2. calculate the change in gravitational potential energy. change = .............................................. J [2] (ii) The cyclist pedals continuously so that the useful power delivered to the bicycle is 75 W. Calculate the useful work done by the cyclist climbing up the slope. work done = .............................................. J [2] (c) Some energy is used in overcoming frictional forces. For Examiner’s (i) Use your answers in (b) to show that the total energy converted in overcoming Use frictional forces is approximately 670 J. [1] (ii) Determine the average magnitude of the frictional forces. average force = ..............................................N [1] (d) Suggest why the magnitude of the total resistive force would not be constant. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2]

Mark scheme: 3 (a) evidence of use of area below the line B1 distance = 39 m (allow ±0.5 m) A2 [3] (if > ±0.5 m but ≤ 1.0 m, then allow 1 mark) (b) (i) 1 EK = ½mv 2 C1 ∆ EK = ½ × 92 × (62 – 32) = 1240 J A1 [2] 2 EP = mgh C1 ∆ EP = 92 × 9.8 × 1.3 = 1170 J A1 [2] (ii) E = Pt C1 E = 75 × 8 = 600 J A1 [2] (c) (i) energy = (1240 + 600) – 1170 M1 = 670 J A0 [1] (ii) force = 670/39 = 17 N A1 [1] (d) frictional forces include air resistance B1 air resistance decreases with decrease of speed B1 [2] GCE AS/A LEVEL – May/June 2010 9702 23

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4 (a) State the evidence for the assumption that For Examiner’s (i) there are significant forces of attraction between molecules in the solid state, Use .................................................................................................................................. ..............................................................................................................................[1] (ii) the forces of attraction between molecules in a gas are negligible. .................................................................................................................................. ..............................................................................................................................[1] (b) Explain, on the basis of the kinetic model of gases, the pressure exerted by a gas. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[4] (c) Liquid nitrogen has a density of 810 kg m–3. The density of nitrogen gas at room temperature and pressure is approximately 1.2 kg m–3. Suggest how these densities relate to the spacing of nitrogen molecules in the liquid and in the gaseous states. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2]

Mark scheme: 4 (a) (i) solid has fixed volume and fixed shape/incompressible B1 [1] (ii) gas fills any space into which it is put B1 [1] (b) atoms/molecules have (elastic) collisions with the walls (of the vessel) B1 momentum of atom/molecule changes B1 so impulse (on wall)/force on wall B1 random motion/many collisions (per unit time) gives rise to (constant) force/pressure B1 [4] (c) spacing (much) greater in gases than in liquids/about ten times C1 either spacing depends on 1/3√ρ or ratio of spacings is about 8.8 A1 [2]

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5 (a) A source of sound has frequency f. Sound of wavelength λ is produced by the source. For Examiner’s (i) State Use 1. what is meant by the frequency of the source, .................................................................................................................................. ..............................................................................................................................[1] 2. the distance moved, in terms of λ, by a wavefront during n oscillations of the source. distance = ..................................................[1] (ii) Use your answers in (i) to deduce an expression for the speed v of the wave in terms of f and λ. [2] (b) The waveform of a sound wave produced on the screen of a cathode-ray oscilloscope (c.r.o.) is shown in Fig. 5.1. 1 cm 1 cm Fig. 5.1 The time-base setting of the c.r.o. is 2.0 ms cm–1. For Examiner’s (i) Determine the frequency of the sound wave. Use frequency = ............................................Hz [2] (ii) A second sound wave has the same frequency as that calculated in (i). The amplitude of the two waves is the same but the phase difference between them is 90°. On Fig. 5.1, draw the waveform of this second wave. [1]

Mark scheme: 5 (a) (i) 1 number of oscillations per unit time (not per second) B1 [1] 2 nλ A1 [1] (ii) v = distance / time = nλ/ t M1 n / t = f hence v= fλ A1 or f oscillations per unit time so fλ is distance per unit time M1 distance per unit time is v so v = fλ A1 [2] (b) (i) 1.0 period is 3 × 2 = 6.0 ms C1 frequency = 1 / (6 × 10–3) = 170 Hz A1 [2] (ii) wave (with approx. same amplitude and) with correct phase difference B1 [1]

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6 (a) (i) State what is meant by an electric current. For Examiner’s .................................................................................................................................. Use ..............................................................................................................................[1] (ii) Define electric potential difference. .................................................................................................................................. ..............................................................................................................................[1] (b) The variation with potential difference V of the current I in a component Y and in a resistor R are shown in Fig. 6.1. 0.7 I / A 0.6 componentcomponentcomponent YYY 0.5 resistor R 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 V / V Fig. 6.1 Use Fig. 6.1 to explain how it can be deduced that resistor R has a constant resistance For of 20 Ω. Examiner’s Use .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2] (c) The component Y and the resistor R in (b) are connected in parallel as shown in Fig. 6.2. E Y R 20 Ω Fig. 6.2 A battery of e.m.f. E and negligible internal resistance is connected across the parallel combination. Use data from Fig. 6.1 to determine (i) the current in the battery for an e.m.f. E of 6.0 V, current = ..............................................A [1] (ii) the total resistance of the circuit for an e.m.f. of 8.0 V. resistance = ............................................. Ω [2] (d) The circuit of Fig. 6.2 is now re-arranged as shown in Fig. 6.3. For Examiner’s Use Y R E Fig. 6.3 The current in the circuit is 0.20 A. (i) Use Fig. 6.1 to determine the e.m.f. E of the battery. E = ..............................................V [1] (ii) Calculate the total power dissipated in component Y and resistor R. power = .............................................W [2]

Mark scheme: 6 (a) (i) movement/flow of charged particles B1 [1] (ii) work done per unit charge (transferred) B1 [1] (b) straight line through origin B1 resistance = V / I , with values for V and I shown M1 = 20 Ω A0 [2] (using the gradient loses the last mark) (c) (i) 0.5 A A1 [1] (ii) either resistance of each resistor is 20 Ω or total current = 0.8 A C1 either combined resistance = 10 Ω or R = E / I = 10 Ω A1 [2] (d) (i) 10 V A1 [1] (ii) power = EI C1 = 10 × 0.2 = 2.0 W A1 [2] GCE AS/A LEVEL – May/June 2010 9702 23

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7 One property of α-particles is that they produce a high density of ionisation of air at For atmospheric pressure. In this ionisation process, a neutral atom becomes an ion pair. The Examiner’s ion pair is a positively-charged particle and an electron. Use (a) State (i) what is meant by an α-particle, .................................................................................................................................. ..............................................................................................................................[1] (ii) an approximate value for the range of α-particles in air at atmospheric pressure. range = ........................................... cm [1] (b) The energy required to produce an ion pair in air at atmospheric pressure is 31 eV. An α-particle has an initial kinetic energy of 8.5 × 10–13 J. (i) Show that 8.5 × 10–13 J is equivalent to 5.3 MeV. [1] (ii) Calculate, to two significant figures, the number of ion pairs produced as the α-particle is stopped in air at atmospheric pressure. number = ..................................................[2] (iii) Using your answer in (a)(ii), estimate the average number of ion pairs produced For per unit length of the track of the α-particle as it is brought to rest in air. Examiner’s Use number per unit length = ..................................................[2]

Mark scheme: 7 (a) (i) either helium nucleus or particle containing two protons and two neutrons B1 [1] (ii) allow any value between 1 cm and 10 cm B1 [1] (b) (i) energy = (8.5 × 10–13)/(1.6 × 10–13) M1 = 5.3 MeV A0 [1] (ii) number = (5.3 × 106)/31 C1 = 1.7 × 105 (allow 2 s.f. only) A1 [2] (iii) number per unit length = (1.7 × 105) / (a)(ii) correct numerical value A1 correct unit B1 [2]

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