Cambridge A Level Physics 9702 — 2012 Oct/Nov Paper 2 · Variant 3

1 (a) The spacing between two atoms in a crystal is 3.8 × 10–10 m. State this distance in pm. spacing = .......................................... pm [1] (b) Calculate the time of one day in Ms. time = .......................................... Ms [1] (c) The distance from the Earth to the Sun is 0.15 Tm. Calculate the time in minutes for light to travel from the Sun to the Earth. time = ......................................... min [2] (d) Underline all the vector quantities in the list below. distance energy momentum weight work [1] (e) The velocity vector diagram for an aircraft heading due north is shown to scale in For Fig. 1.1. There is a wind blowing from the north-west. Examiner’s Use wind 45° aircraft Fig. 1.1 The speed of the wind is 36 m s–1 and the speed of the aircraft is 250 m s–1. (i) Draw an arrow on Fig. 1.1 to show the direction of the resultant velocity of the aircraft. [1] (ii) Determine the magnitude of the resultant velocity of the aircraft. resultant velocity = ...................................... m s–1 [2]

Mark scheme: 1 (a) spacing = 380 or 3.8 × 102 pm B1 [1] (b) time = 24 × 3600 time = 0.086 (0.0864) Ms B1 [1] 1.5 × 10 11 (c) time = distance / speed = C1 3 × 10 8 = 500 (s) = 8.3 min A1 [2] (d) momentum and weight B1 [1] (e) (i) arrow to the right of plane direction (about 4° to 24°) B1 [1] (ii) scale diagram drawn or use of cosine formula v2 = 2502 + 362 – 2 × 250 × 36 × cos 45° or resolving v = [(36 cos 45°)2 + (250 – 36 sin 45°)2]1/2 C1 resultant velocity = 226 (220 – 240 for scale diagram) m s–1 allow one mark for values 210 to 219 or 241 to 250 m s–1 or use of formula (v2 = 51068) v = 230 (226) m s–1 A1 [2]

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2 Two planks of wood AB and BC are inclined at an angle of 15° to the horizontal. The two For wooden planks are joined at point B, as shown in Fig. 2.1. Examiner’s Use M C A 0.26 m 0.26 m 15° B 15° Fig. 2.1 A small block of metal M is released from rest at point A. It slides down the slope to B and up the opposite side to C. Points A and C are 0.26 m above B. Assume frictional forces are negligible. (a) (i) Describe and explain the acceleration of M as it travels from A to B and from B to C. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................ [3] (ii) Calculate the time taken for M to travel from A to B. time = ............................................. s [3] (iii) Calculate the speed of M at B. speed = ...................................... m s–1 [2] (b) The plank BC is adjusted so that the angle it makes with the horizontal is 30°. M is released from rest at point A and slides down the slope to B. It then slides a distance along the plank from B towards C. Use the law of conservation of energy to calculate this distance. Explain your working. distance = ............................................ m [2]

Mark scheme: 2 (a) (i) accelerations (A to B and B to C) are same magnitude B1 accelerations (A to B and B to C) are opposite directions or both accelerations are toward B B1 (A to B and B to C) the component of the weight down the slope provides the acceleration B1 [3] (ii) acceleration = g sin15 ° C1 s = 0 + ½ at2 s = 0.26 / sin 15 ° = 1.0 C1 2 1 . 0 × 2 t = t = 0.89 s A1 [3] 9 . 8 × sin15 ° (iii) v = 0 + g sin15t or v2 = 0 + 2g sin15 × 1.0 C1 v = 2.26 m s–1 A1 [2] (using loss of GPE = gain KE can score full marks) (b) loss of GPE at A = gain in GPE at C or loss of KE at B = gain in GPE at C B1 h1 = h2 = 0.26 m or ½ mv2 = mgh h2 = 0.5 × (2.26)2 / 9.81 = 0.26 m x = 0.26 / sin 30° = 0.52 m A1 [2]

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3 (a) Define power. For Examiner’s .......................................................................................................................................... Use .................................................................................................................................... [1] (b) A cyclist travels along a horizontal road. The variation with time t of speed v is shown in Fig. 3.1. 12.0 10.0 8.0 v / m s–1 6.0 4.0 2.0 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 t / s Fig. 3.1 The cyclist maintains a constant power and after some time reaches a constant speed of 12 m s–1. (i) Describe and explain the motion of the cyclist. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................ [3] (ii) When the cyclist is moving at a constant speed of 12 m s–1 the resistive force is For 48 N. Show that the power of the cyclist is about 600 W. Explain your working. Examiner’s Use [2] (iii) Use Fig. 3.1 to show that the acceleration of the cyclist when his speed is 8.0 m s–1 is about 0.5 m s–2. [2] (iv) The total mass of the cyclist and bicycle is 80 kg. Calculate the resistive force R acting on the cyclist when his speed is 8.0 m s–1. Use the value for the acceleration given in (iii). R = ............................................ N [3] (v) Use the information given in (ii) and your answer to (iv) to show that, in this situation, the resistive force R is proportional to the speed v of the cyclist. [1]

Mark scheme: 3 (a) power is the rate of doing work or power = work done / time (taken) or power = energy transferred / time (taken) B1 [1] (b) (i) as the speed increases drag / air resistance increases B1 resultant force reduces hence acceleration is less B1 constant speed when resultant force is zero B1 [3] (allow one mark for speed increases and acceleration decreases) GCE AS/A LEVEL – October/November 2012 9702 23 (ii) force from cyclist = drag force / resistive force B1 P = 12 × 48 M1 P = 576 W A0 [2] (iii) tangent drawn at speed = 8.0 m s–1 M1 gradient values that show acceleration between 0.44 to 0.48 m s–2 A1 [2] (iv) F – R = ma C1 600 / 8 – R = 80 × 0.5 [using P = 576] 576 / 8 – R = 80 × 0.5 C1 R = 75 – 40 = 35 N R = 72 – 40 = 32 N A1 [3] (v) at 12 m s–1 drag is 48 N, at 8 m s–1 drag is 35 or 32 N R / v calculated as 4 and 4 or 4.4 and consistent response for whether R is proportional to v or not B1 [1]

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4 A circuit used to measure the power transfer from a battery is shown in Fig. 4.1. The power is For transferred to a variable resistor of resistance R. Examiner’s Use E r A I R V Fig. 4.1 The battery has an electromotive force (e.m.f.) E and an internal resistance r. There is a potential difference (p.d.) V across R. The current in the circuit is І. (a) By reference to the circuit shown in Fig. 4.1, distinguish between the definitions of e.m.f. and p.d. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .................................................................................................................................... [3] (b) Using Kirchhoff’s second law, determine an expression for the current І in the circuit. [1] (c) The variation with current І of the p.d. V across R is shown in Fig. 4.2. For Examiner’s 6.0 Use 4.0 V / V 2.0 0 0 1.0 2.0 3.0 4.0 I /A Fig. 4.2 Use Fig. 4.2 to determine (i) the e.m.f. E, E = ............................................ V [1] (ii) the internal resistance r. r = ............................................ Ω [2] (d) (i) Using data from Fig. 4.2, calculate the power transferred to R for a current of 1.6 A. power = ........................................... W [2] (ii) Use your answers from (c)(i) and (d)(i) to calculate the efficiency of the battery for a current of 1.6 A. efficiency = ........................................... % [2]

Mark scheme: 4 (a) e.m.f. = chemical energy to electrical energy M1 p.d. = electrical energy to thermal energy M1 idea of per unit charge A1 [3] (b) E = I (R +r) or I = E / (R +r) (any subject) B1 [1] (c) (i) E = 5.8 V B1 [1] (ii) evidence of gradient calculation or calculation with values from graph e.g. 5.8 = 4 + 1.0 × r C1 r = 1.8 Ω A1 [2] (d) (i) P = VI C1 P = 2.9 × 1.6 = 4.6 (4.64) W A1 [2] (ii) power from battery = 1.6 × 5.8 = 9.28 or efficiency = VI / EI C1 efficiency = (4.64 / 9.28) × 100 = 50 % or (2.9 / 5.8) × 100 = 50% A1 [2]

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5 (a) State one property of electromagnetic waves that is not common to other transverse For waves. Examiner’s Use .................................................................................................................................... [1] (b) The seven regions of the electromagnetic spectrum are represented by blocks labelled A to G in Fig. 5.1. visible region A B C D E F G wavelength decreasing Fig. 5.1 A typical wavelength for the visible region D is 500 nm. (i) Name the principal radiations and give a typical wavelength for each of the regions B, E and F. B: name: ............................................ wavelength: ............................................. m E: name: ............................................ wavelength: ............................................. m F: name: ............................................ wavelength: ............................................. m [3] (ii) Calculate the frequency corresponding to a wavelength of 500 nm. frequency = .......................................... Hz [2] (c) All the waves in the spectrum shown in Fig. 5.1 can be polarised. Explain the meaning of the term polarised. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .................................................................................................................................... [2]

Mark scheme: 5 (a) travel through a vacuum / free space B1 [1] (b) (i) B : name: microwaves wavelength: 10– 4 to 10–1 m B1 C : name: ultra-violet / UV wavelength: 10–7 to 10–9 m B1 F : name: X –rays wavelength: 10–9 to 10–12 m B1 [3] 3 × 10 8 (ii) f = C1 500 × 10 − 9 f = 6(.0) × 1014 Hz A1 [2] GCE AS/A LEVEL – October/November 2012 9702 23 (c) vibrations are in one direction M1 perpendicular to direction of propagation / energy transfer or good sketch showing this A1 [2]

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6 (a) β-radiation is emitted during the spontaneous radioactive decay of an unstable nucleus. For Examiner’s (i) State the nature of a β-particle. Use ............................................................................................................................ [1] (ii) State two properties of β-radiation. 1. ............................................................................................................................... 2. ............................................................................................................................... [2] (iii) Explain the meaning of spontaneous radioactive decay. .................................................................................................................................. ............................................................................................................................ [1] (b) The following equation represents the decay of a nucleus of hydrogen-3 by the emission of a β-particle. Complete the equation. ...... ...... 31H He + β [2] ...... ...... (c) The β-particle is emitted with an energy of 5.7 × 103 eV. Calculate the speed of the β-particle. speed = ...................................... m s–1 [3] (d) A different isotope of hydrogen is hydrogen-2 (deuterium). Describe the similarities and differences between the atoms of hydrogen-2 and hydrogen-3. .......................................................................................................................................... .......................................................................................................................................... .................................................................................................................................... [2]

Mark scheme: 6 (a) (i) electron B1 [1] (ii) any two: can be deflected by electric and magnetic fields or negatively charged / absorbed by few (1 – 4) mm of aluminum / 0.5 to 2 m or metres for range in air / speed up to 0.99c / range of speeds / energies B2 [2] (iii) decay occurs and cannot be affected by external / environmental factors or two stated factors such as chemical / pressure / temperature / humidity B1 [1] (b) 3 and 0 for superscript numbers B1 2 and –1 for subscript numbers B1 [2] (c) energy = 5.7 × 103 × 1.6 × 10–19 (= 9.12 × 10–16 J) C1 2 × 9.12 × 10 −16 v2 = C1 9.11 × 10 − 31 v = 4.5 × 107 m s–1 A1 [3] (d) both have 1 proton and 1 electron B1 1 neutron in hydrogen-2 and 2 neutrons in hydrogen-3 B1 [2] (special case: for one mark ‘same number of protons / atomic number different number of neutrons’)

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