Cambridge A Level Physics 9702 — 2009 Oct/Nov Paper 2 · Variant 2

1 A simple pendulum may be used to determine a value for the acceleration of free fall g. Measurements are made of the length L of the pendulum and the period T of oscillation. The values obtained, with their uncertainties, are as shown. T = (1.93 ± 0.03) s L = (92 ± 1) cm (a) Calculate the percentage uncertainty in the measurement of (i) the period T, uncertainty = ............................................ % [1] (ii) the length L. uncertainty = ............................................ % [1] (b) The relationship between T, L and g is given by For Examiner’s 4 2L Use g = 2 . T Using your answers in (a), calculate the percentage uncertainty in the value of g. uncertainty = ............................................ % [1] (c) The values of L and T are used to calculate a value of g as 9.751 m s–2. (i) By reference to the measurements of L and T, suggest why it would not be correct to quote the value of g as 9.751 m s–2. .................................................................................................................................. ............................................................................................................................ [1] (ii) Use your answer in (b) to determine the absolute uncertainty in g. Hence state the value of g, with its uncertainty, to an appropriate number of significant figures. g = .......................... ± ........................ m s–2 [2]

Mark scheme: 1 (a) (i) either 1.55% or 1.6% …(not 1.5 or 2) ............................................ A1 [1] (ii) either 1.09% or 1.1% …(not 1.0 or 1) ............................................ A1 [1] (b) answer of {(ii) + 2 × (i)} to any number of sig. fig. either 4.2% or 4.3% .................................................................................... A1 [1] (c) (i) either the value has more significant figures than the data or uncertainty of ±0.4 renders more than 2 s.f. meaningless) ......................... B1 [1] (ii) uncertainty in g = ±0.41 / ±0.42 to any number of s.f. ....................................C1 g = (9.8 ± 0.4) m s-2 ........................................................................................ A1 [2] [Total: 6]

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2 (a) (i) State one similarity between the processes of evaporation and boiling. For Examiner’s .................................................................................................................................. Use ............................................................................................................................ [1] (ii) State two differences between the processes of evaporation and boiling. 1. ............................................................................................................................... .................................................................................................................................. 2. ............................................................................................................................... .................................................................................................................................. [4] (b) Titanium metal has a density of 4.5 g cm–3. A cube of titanium of mass 48 g contains 6.0 × 1023 atoms. (i) Calculate the volume of the cube. volume = ......................................... cm3 [1] (ii) Estimate For Examiner’s 1. the volume occupied by each atom in the cube, Use volume = ......................................... cm3 [1] 2. the separation of the atoms in the cube. separation = .......................................... cm [1]

Mark scheme: 2 (a) (i) e.g. (phase) change from liquid to gas / vapour thermal energy required to maintain constant temperature ......................... B1 [1] (do not allow ‘convert water to steam’) (ii) e.g. evaporation takes place at surface .............................................................. B1 boiling takes place in body of the liquid ....................................................... B1 e.g. evaporation occurs at all temperatures ....................................................... B1 boiling occurs at one temperature ............................................................... B1 [4] 48 (b) (i) volume = ( =) 10.7 cm3 .............................................................................. A1 [1] 4.5 (ii) 1 volume = 10.7 / (6.0 × 1023) = 1.8 × 10-23 cm3 ................................................................................................ A1 [1] 2 separation = 3√(1.8 × 10-23) = 2.6 × 10-8 cm ................................................................................................... A1 [1] [Total: 8] 1

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3 A small ball is thrown horizontally with a speed of 4.0 m s–1. It falls through a vertical height of For 1.96 m before bouncing off a horizontal plate, as illustrated in Fig. 3.1. Examiner’s Use 4.0 m s–1 1.96 m 0.98 m plate Fig. 3.1 Air resistance is negligible. (a) For the ball, as it hits the horizontal plate, (i) state the magnitude of the horizontal component of its velocity, horizontal velocity = ....................................... m s–1 [1] (ii) show that the vertical component of the velocity is 6.2 m s–1. [1] (b) The components of the velocity in (a) are both vectors. For Examiner’s Complete Fig. 3.2 to draw a vector diagram, to scale, to determine the velocity of the Use ball as it hits the horizontal plate. Fig. 3.2 velocity = .............................................m s–1] at ............................. ° to the vertical [3] (c) After bouncing on the plate, the ball rises to a vertical height of 0.98 m. (i) Calculate the vertical component of the velocity of the ball as it leaves the plate. vertical velocity = ....................................... m s–1 [2] (ii) The ball of mass 34 g is in contact with the plate for a time of 0.12 s. For Examiner’s Use your answer in (c)(i) and the data in (a)(ii) to calculate, for the ball as it bounces Use on the plate, 1. the change in momentum, change = ................................... kg m s–1 [3] 2. the magnitude of the average force exerted by the plate on the ball due to this momentum change. force = ............................................. N [2]

Mark scheme: 3 (a) (i) speed = 4.0 m s-1 …(allow 1 s.f.) ................................................................... A1 [1] (ii) v2 = 2gh = 2 × 9.8 × 1.96 .............................................................................................M1 v = 6.2 m s-1 ..................................................................................................... A0 [1] (use of g = 10 m s-2 loses the mark) (b) correct basic shape with correct directions for vectors ..............................................M1 speed = (7.4 ± 0.2) m s-1 ......................................................................................... A1 at (33 ± 2)° to the vertical .......................................................................................... A1 [3] (for credit to be awarded, speed and angle must be correct on the diagram – not calculated) GCE A/AS LEVEL – October/November 2009 9702 22 (c) (i) either v2 = 2 × 9.8 × 0.98 or v = 6.2 / √2 ............................................C1 speed = 4.4 m s-1 .............................................................................................. A1 [2] (allow calculation of t = 0.447 s, then v = 4.4 m s-1) (ii) 1 momentum = mv ...........................................................................................C1 change in momentum = 0.034 (6.2 + 4.4) ........................................................C1 = 0.36 kg m s-1 .............................................................. A1 [3] (use of 0.034 (6.2 - 4.4) loses last two marks) 2 force = ∆p / ∆t …….(however expressed) ...................................................C1 0.36 = 0.12 = 3.0 N ……(allow 1 s.f.) ................................................................... A1 [2] [Total: 12]

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4 (a) Explain what is meant by strain energy (elastic potential energy). For Examiner’s .......................................................................................................................................... Use .......................................................................................................................................... .................................................................................................................................... [2] (b) A spring that obeys Hooke’s law has a spring constant k. Show that the energy E stored in the spring when it has been extended elastically by an amount x is given by E = 12kx 2. [3] (c) A light spring of unextended length 14.2 cm is suspended vertically from a fixed point, For as illustrated in Fig. 4.1. Examiner’s Use fixed point fixed point fixed point 14.2 cm 16.3 cm 17.8 cm 3.8 N F 3.8 N Fig. 4.1 Fig. 4.2 Fig. 4.3 A mass of weight 3.8 N is hung from the end of the spring, as shown in Fig. 4.2. The length of the spring is now 16.3 cm. An additional force F then extends the spring so that its length becomes 17.8 cm, as shown in Fig. 4.3. The spring obeys Hooke’s law and the elastic limit of the spring is not exceeded. (i) Show that the spring constant of the spring is 1.8 N cm–1. [1] (ii) For the extension of the spring from a length of 16.3 cm to a length of 17.8 cm, For Examiner’s 1. calculate the change in the gravitational potential energy of the mass on the Use spring, change in energy = ............................................. J [2] 2. show that the change in elastic potential energy of the spring is 0.077 J, [1] 3. determine the work done by the force F. work done = ............................................. J [1]

Mark scheme: 4 (a) ability to do work ........................................................................................................ B1 as a result of a change of shape of an object/stretched etc ...................................... B1 [2] (b) work = average force ×distance moved (in direction of the force) ........................... B1 either work = ½ × F × x or work is area under F/x graph which is ½Fx ................................................. B1 F = kx ........................................................................................................................ B1 so work / energy = ½kx2 .......................................................................................... A0 [3] 3.8 (c) (i) spring constant = .....................................................................................M1 2.1 = 1.8 N cm-1 ........................................................................... A0 [1] (ii) 1 ∆EP = mg∆h or W∆h ...................................................................................C1 = 3.8 × 1.5 × 10-2 = 0.057 J ................................................................................................ A1 [2] 2 ∆ES = ½ × 1.8 × 102 (0.0362 – 0.0212) ...........................................................M1 = 0.077 J ................................................................................................ A0 [1] 3 work done = 0.077 – 0.057 = 0.020 J ....................................................................................... A1 [1] (allow e.c.f. if ∆ES > ∆EP) [Total: 10] GCE A/AS LEVEL – October/November 2009 9702 22

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5 A uniform string is held between a fixed point P and a variable-frequency oscillator, as shown For in Fig. 5.1. Examiner’s Use L 1 8 L X P Y oscillator 1 8 L Fig. 5.1 The distance between point P and the oscillator is L. The frequency of the oscillator is adjusted so that the stationary wave shown in Fig. 5.1 is formed. Points X and Y are two points on the string. 1 Point X is a distance 8L from the end of the string attached to the oscillator. It vibrates with frequency f and amplitude A. 1 Point Y is a distance 8L from the end P of the string. (a) For the vibrations of point Y, state (i) the frequency (in terms of f ), frequency = ................................................ [1] (ii) the amplitude (in terms of A). amplitude = ................................................ [1] (b) State the phase difference between the vibrations of point X and point Y. phase difference = ................................................ [1] (c) (i) State, in terms of f and L, the speed of the wave on the string. For Examiner’s speed = ................................................ [1] Use (ii) The wave on the string is a stationary wave. Explain, by reference to the formation of a stationary wave, what is meant by the speed stated in (i). .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................ [3]

Mark scheme: 5 (a) (i) frequency f ......................................................................................................... B1 [1] (ii) amplitude A ....................................................................................................... B1 [1] (b) π rad or 180° ………(unit necessary) .................................................................... B1 [1] (c) (i) speed = f × L ..................................................................................................... B1 [1] (ii) wave is reflected at end / at P ............................................................................ B1 either incident and reflected waves interfere or two waves travelling in opposite directions interfere ................................M1 speed is the speed of incident or reflected wave / one of these waves .............. A1 [3] [Total: 7]

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6 (a) Two resistors, each of resistance R, are connected first in series and then in parallel. For Examiner’s Show that the ratio Use combined resistance of resistors connected in series combined resistance of resistors connected in parallel is equal to 4. [1] (b) The variation with potential difference V of the current I in a lamp is shown in Fig. 6.1. 0.15 I / A 0.10 0.05 0 0 1.0 2.0 3.0 V / V Fig. 6.1 Calculate the resistance of the lamp for a potential difference across the lamp of 1.5 V. For Examiner’s Use resistance = ............................................ [2] (c) Two lamps, each having the I-V characteristic shown in Fig. 6.1, are connected first in series and then in parallel with a battery of e.m.f. 3.0 V and negligible internal resistance. Complete the table of Fig. 6.2 for the lamps connected to the battery. p.d. across resistance of combined resistance each lamp / V each lamp / of lamps / lamps connected in series lamps connected in parallel Fig. 6.2 [4] (d) (i) Use data from the completed Fig. 6.2 to calculate the ratio combined resistance of lamps connected in series . combined resistance of lamps connected in parallel ratio = ................................................ [1] (ii) The ratios in (a) and (d)(i) are not equal. By reference to Fig. 6.1, state and explain qualitatively the change in the resistance of a lamp as the potential difference is changed. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................ [3]

Mark scheme: 6 (a) total resistance in series = 2R total resistance in parallel = ½R ................................................................................M1 ratio is 2R / ½R = 4 ......(allow mark if clear numbers in the ratio) ........................ A0 [1] (b) at 1.5 V, current is 0.10 A ..........................................................................................C1 1.5 resistance = V/I = 0.1 = 15 Ω .................................................................................................... A1 [2] (use of tangent or any other current scores no marks) (c) p.d. across resistance of combined each lamp / V each lamp / Ω resistance / Ω series 1.5 15 30 parallel 3.0 20 10 column 1 .................................................................................................................... A1 columns 2 and 3: max 3 marks with -1 mark for each error or omission .................. A3 [4] (d) (i) ratio is 3 ...............(allow e.c.f.) ......................................................................... A1 [1] (ii) resistance increases as potential difference increases ...................................... B1 increasing p.d. increases current ........................................................................ B1 current increases non-linearly so resistance increases ..................................... B1 [3] [Total: 11] GCE A/AS LEVEL – October/November 2009 9702 22

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For7 Tungsten-184 (18474 W) and tungsten-185 (18574 W) are two isotopes of tungsten. Examiner’s Use Tungsten-184 is stable but tungsten-185 undergoes -decay to form rhenium (Re). (a) Explain what is meant by isotopes. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .................................................................................................................................... [2] (b) The -decay of nuclei of tungsten-185 is spontaneous and random. State what is meant by (i) spontaneous decay, .................................................................................................................................. ............................................................................................................................ [1] (ii) random decay. .................................................................................................................................. ............................................................................................................................ [1] (c) Complete the nuclear equation for the -decay of a tungsten-185 nucleus. 185 74 W [2]

Mark scheme: 7 (a) either forms of same element or atoms / nuclei with same number of protons ................................................M1 atoms / nuclei contain different numbers of neutrons ................................................ A1 [2] (use of ‘element’ rather than atoms / nuclei scores max 1 mark) (b) (i) decay is not affected by environmental factors .................................................. B1 [1] (allow two named factors) (ii) either time of decay (of a nucleus) cannot be predicted or nucleus has constant probability in a given time .................................. B1 [1] (c) 18575 Re ......................................................................................................................... B1 either −01 e or −β01 ......................................................................................... B1 [2] [Total: 6]

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