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

1 A metal wire has a cross-section of diameter approximately 0.8 mm. (a) State what instrument should be used to measure the diameter of the wire. ......................................................................................................................................[1] (b) State how the instrument in (a) is (i) checked so as to avoid a systematic error in the measurements, .................................................................................................................................. ..............................................................................................................................[1] (ii) used so as to reduce random errors. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[2]

Mark scheme: 1 (a) micrometer/screw gauge/digital callipers ………………………………………. B1 [1] (b) (i) look/check for zero error ……………………………………………………. B1 [1] (ii) take several readings ……………………………………………………….. M1 around the circumference/along the wire …………………………………. A1 [2]

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2 (a) The distance s moved by an object in time t may be given by the expression For Examiner’s s = 12at 2 Use where a is the acceleration of the object. State two conditions for this expression to apply to the motion of the object. 1. ...................................................................................................................................... .......................................................................................................................................... 2. ...................................................................................................................................... .......................................................................................................................................... [2] (b) A student takes a photograph of a steel ball of radius 5.0 cm as it falls from rest. The image of the ball is blurred, as illustrated in Fig. 2.1. The image is blurred because the ball is moving while the photograph is being taken. initial position 80 of ball in photograph cm final position 90 of ball in photograph cm 100 cm Fig. 2.1 The scale shows the distance fallen from rest by the ball. At time t = 0, the top of the ball is level with the zero mark on the scale. Air resistance is negligible. Calculate, to an appropriate number of significant figures, For Examiner’s (i) the time the ball falls before the photograph is taken, Use time = ............................................ s [3] (ii) the time interval during which the photograph is taken. time interval = ............................................. s [3] (c) The student in (b) takes a second photograph starting at the same position on the scale. The ball has the same radius but is less dense, so that air resistance is not negligible. State and explain the changes that will occur in the photograph. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2]

Mark scheme: 2 (a) e.g. initial speed is zero constant acceleration straight line motion (any two, one mark each) ……………………………………………………………….B2 [2] (b) (i) s = ½a t 2 0.79 = ½ × 9.8 × t 2 ………………………………………………………….. C1 t = 0.40 s allow 1 SF or greater ……………………………………………. A1 2 or 3 SF answer ……………………………………………………….. A1 [3] (ii) distance travelled by end of time interval = 90 cm ………………………. C1 0.90 = ½ × 9.8 × t 2 t = 0.43 s allow 2 SF or greater ……………………………………………. C1 time interval = 0.03 s ………………………………………………………... A1 [3] (c) (air resistance) means ball’s speed/acceleration is less ……………………… M1 length of image is shorter ………………………………………………………… A1 [2]

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3 (a) (i) Define force. For Examiner’s .................................................................................................................................. Use ..............................................................................................................................[1] (ii) State Newton’s third law of motion. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[3] (b) Two spheres approach one another along a line joining their centres, as illustrated in Fig. 3.1. sphere sphere A B Fig. 3.1 When they collide, the average force acting on sphere A is FA and the average force acting on sphere B is FB. The forces act for time tA on sphere A and time tB on sphere B. (i) State the relationship between 1. FA and FB, ..............................................................................................................................[1] 2. tA and tB. ..............................................................................................................................[1] (ii) Use your answers in (i) to show that the change in momentum of sphere A is equal in magnitude and opposite in direction to the change in momentum of sphere B. .................................................................................................................................. ..............................................................................................................................[1] (c) For the spheres in (b), the variation with time of the momentum of sphere A before, For during and after the collision with sphere B is shown in Fig. 3.2. Examiner’s Use 151515 momentum to right / N s 101010 spherespheresphere AAA 55 00 timetimetime spherespheresphere BBB –-5-55 –10-10-10 –15-15-15 Fig. 3.2 The momentum of sphere B before the collision is also shown on Fig. 3.2. Complete Fig. 3.2 to show the variation with time of the momentum of sphere B during and after the collision with sphere A. [3]

Mark scheme: 3 (a) (i) force is rate of change of momentum ………………………………………… B1 [1] (ii) force on body A is equal in magnitude to force on body B (from A) …………M1 forces are in opposite directions ……………………………………………… A1 forces are of the same kind ………………………………………………………A1 [3] (b) (i) 1 FA = – FB ……………………………………………………………………. B1 [1] 2 t A = t B ……………………………………………………………………… B1 [1] (ii) ∆p = FA t A = – FB t B ………………………………………………………….. B1 [1] (c) graph: momentum change occurs at same times for both spheres …………. B1 final momentum of sphere B is to the right …………………………………….. M1 and of magnitude 5 N s …………………………………………………………… A1 [3]

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4 (a) State two features of a stationary wave that distinguish it from a progressive wave. For Examiner’s 1. ...................................................................................................................................... Use .......................................................................................................................................... 2. ...................................................................................................................................... .......................................................................................................................................... [2] (b) A long tube is open at one end. It is closed at the other end by means of a piston that can be moved along the tube, as shown in Fig. 4.1. tube piston loudspeaker L Fig. 4.1 A loudspeaker producing sound of frequency 550 Hz is held near the open end of the tube. The piston is moved along the tube and a loud sound is heard when the distance L between the piston and the open end of the tube is 45 cm. The speed of sound in the tube is 330 m s–1. (i) Show that the wavelength of the sound in the tube is 60 cm. [1] (ii) On Fig. 4.1, mark all the positions along the tube of 1. the displacement nodes (label these with the letter N), 2. the displacement antinodes (label these with the letter A). [3] (c) The frequency of the sound produced by the loudspeaker in (b) is gradually reduced. For Examiner’s Determine the lowest frequency at which a loud sound will be produced in the tube of Use length L = 45 cm. frequency = .......................................... Hz [3]

Mark scheme: 4 (a) e.g. no energy transfer amplitude varies along its length/nodes and antinodes neighbouring points (in inter-nodal loop) vibrate in phase, etc. (any two, 1 mark each to max 2 ………………………………………………………..B2 [2] GCE AS/A LEVEL – May/June 2010 9702 22 (b) (i) λ = (330 × 102)/550 ………………………………………………………….. M1 λ = 60 cm ……………………………………………………………………… A0 [1] (ii) node labelled at piston ………………………………………………………. B1 antinode labelled at open end of tube ……………………………………… B1 additional node and antinode in correct positions along tube …………… B1 [3] (c) at lowest frequency, length = λ/4 ………………………………………………... C1 λ = 1.8 m frequency = 330/1.8 ………………………………………………………………. C1 = 180 Hz ………………………………………………………………………….... A1 [3]

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5 (a) Tensile forces are applied to opposite ends of a copper rod so that the rod is stretched. For The variation with stress of the strain of the rod is shown in Fig. 5.1. Examiner’s Use 2.5 stress / 108 Pa 2.0 1.5 1.0 0.5 0 0 1.0 2.0 3.0 4.0 5.0 strain / 10–3 Fig. 5.1 (i) Use Fig. 5.1 to determine the Young modulus of copper. Young modulus = .......................................... Pa [3] (ii) On Fig. 5.1, sketch a line to show the variation with stress of the strain of the rod as the stress is reduced from 2.5 × 106 Pa to zero. No further calculations are expected. [1] (b) The walls of the tyres on a car are made of a rubber compound. For The variation with stress of the strain of a specimen of this rubber compound is shown Examiner’s in Fig. 5.2. Use stress 0 0 strain Fig. 5.2 As the car moves, the walls of the tyres bend and straighten continuously. Use Fig. 5.2 to explain why the walls of the tyres become warm. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[3]

Mark scheme: 5 (a) (i) Young modulus = stress/strain ……………………………………………… C1 data chosen using point in linear region of graph ………………………… M1 Young modulus = (2.1 × 108)/(1.9 × 10–3) = 1.1 × 1011 Pa ……………………………………………………………….. A1 [3] (ii) This mark was removed from the assessment, owing to a power-of-ten inconsistency in the printed question paper. (b) area between lines represents energy/area under curve represents energy .. M1 when rubber is stretched and then released/two areas are different ……...... A1 this energy seen as thermal energy/heating/difference represents energy released as heat …………………………………………………………………… A1 [3] 2 2

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6 (a) A metal wire of constant resistance is used in an electric heater. For In order not to overload the circuit for the heater, the supply voltage to the heater is Examiner’s reduced from 230 V to 220 V. Use Determine the percentage reduction in the power output of the heater. reduction = ............................................ % [2] (b) A uniform wire AB of length 100 cm is connected between the terminals of a cell of e.m.f. 1.5 V and negligible internal resistance, as shown in Fig. 6.1. 1.5 V 100 cm C A B L 5.0 Ω A Fig. 6.1 An ammeter of internal resistance 5.0 Ω is connected to end A of the wire and to a contact C that can be moved along the wire. Determine the reading on the ammeter for the contact C placed (i) at A, reading = ............................................. A [1] (ii) at B. For Examiner’s Use reading = ............................................ A [1] (c) Using the circuit in (b), the ammeter reading I is recorded for different distances L of the contact C from end A of the wire. Some data points are shown on Fig. 6.2. 0.4 I / A 0.3 0.2 0.1 0 0 20 40 60 80 100 L / cm Fig. 6.2 (i) Use your answers in (b) to plot data points on Fig. 6.2 corresponding to the contact C placed at end A and at end B of the wire. [1] (ii) Draw a line of best fit for all of the data points and hence determine the ammeter reading for contact C placed at the midpoint of the wire. reading = .............................................. A [1] (iii) Use your answer in (ii) to calculate the potential difference between A and the For contact C for the contact placed at the midpoint of AB. Examiner’s Use potential difference = .............................................. V [2] (d) Explain why, although the contact C is at the midpoint of wire AB, the answer in (c)(iii) is not numerically equal to one half of the e.m.f. of the cell. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2]

Mark scheme: 6 (a) either P ∝ V 2 or P = V 2/R …………………………………………………………. C1 reduction = (2302 – 2202)/2302 = 8.5 % ………………………………………………………………….. A1 [2] (b) (i) zero ……………………………………………………………………………. A1 [1] (ii) 0.3(0) A ……………………………………………………………………….. A1 [1] (c) (i) correct plots to within ± 1 mm ………………………………………………. B1 [1] (ii) reasonable line/curve through points giving current as 0.12 A allow ± 0.005A) ………………………………………………………………. B1 [1] (iii) V = IR …………………………………………………………………………. C1 V = 0.12 × 5.0 = 0.6(0) V …………………………………………………………………... A1 [2] (d) circuit acts as a potential divider/current divides/current in AC not the same as current in BC ………………………………………………………………………. B1 resistance between A and C not equal to resistance between C and B ……. B1 or current in wire AC × R is not equal to current in wire BC × R B1 [2] any 2 statements GCE AS/A LEVEL – May/June 2010 9702 22

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7 (a) The radioactive decay of some nuclei gives rise to the emission of α-particles. For State Examiner’s Use (i) what is meant by an α-particle, ..............................................................................................................................[1] (ii) two properties of α-particles. 1. ............................................................................................................................... .................................................................................................................................. 2. ............................................................................................................................... .................................................................................................................................. [2] (b) One possible nuclear reaction involves the bombardment of a stationary nitrogen-14 nucleus by an α-particle to form oxygen-17 and another particle. (i) Complete the nuclear equation for this reaction. 14 ...... 17 N + O + ................. [2] 7 8 ......α (ii) The total mass-energy of the nitrogen-14 nucleus and the α-particle is less than that of the particles resulting from the reaction. This mass-energy difference is 1.1 MeV. 1. Suggest how it is possible for mass-energy to be conserved in this reaction. ............................................................................................................................. .........................................................................................................................[1] 2. Calculate the speed of an α-particle having kinetic energy of 1.1 MeV. speed = ....................................... m s–1 [4]

Mark scheme: 7 (a) (i) either helium nucleus or contains 2 protons and 2 neutrons ………………………………… B1 [1] (ii) e.g. range is a few cm in air/sheet of thin paper speed up to 0.1 c causes dense ionisation in air positively charged or deflected in magnetic or electric fields (any two, 1 each to max 2) ………………………………………………….. B2 [2] (b) (i) 42 α ……………………………………………………………………………… B1 either 11 p or 11 H ……………………………………………………………….. B1 [2] (ii) 1 initially, α-particle must have some kinetic energy ………………….. B1 [1] (ii) 2 1.1 MeV = 1.1 × 1.6 × 10–13 = 1.76 × 10–13 J …………………………. C1 EK = ½mv 2 ……………………………………………………………….. C1 1.76 × 10–13 = ½ × 4 × 1.66 × 10–27 × v 2 ……………………………… C1 v = 7.3 × 106 m s–1 ……………………………………………………..... A1 [4] use of 1.67 × 10–27 kg for mass is a maximum of 3/4

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