Cambridge A Level Physics 9702 — 2011 Oct/Nov Paper 2 · Variant 2

1 The variation with time t of the displacement s for a car is shown in Fig. 1.1. 600 500 s / m 400 300 200 100 0 0 20 40 60 80 100 t / s Fig. 1.1 (a) Determine the magnitude of the average velocity between the times 5.0 s and 35.0 s. average velocity = ........................................ m s–1 [2] (b) On Fig. 1.2, sketch the variation with time t of the velocity v for the car. v / m s–1 0 0 20 40 60 80 100 t / s Fig. 1.2 [4]

Mark scheme: 1 (a) average velocity = 540 / 30 C1 = 18 m s–1 A1 [2] (b) velocity zero at time t = 0 B1 positive value and horizontal line for time t = 5 s to 35 s B1 line / curve through v = 0 at t = 45 s to negative velocity B1 negative horizontal line from 53 s with magnitude less than positive value and horizontal line to time = 100 s B1 [4]

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2 (a) Define For Examiner’s (i) force, Use .................................................................................................................................. ..............................................................................................................................[1] (ii) work done. .................................................................................................................................. ..............................................................................................................................[1] (b) A force F acts on a mass m along a straight line for a distance s. The acceleration of the mass is a and the speed changes from an initial speed u to a final speed v. (i) State the work W done by F. [1] (ii) Use your answer in (i) and an equation of motion to show that kinetic energy of a mass can be given by the expression kinetic energy = ½ × mass × (speed)2. [3] (c) A resultant force of 3800 N causes a car of mass of 1500 kg to accelerate from an initial speed of 15 m s–1 to a final speed of 30 m s–1. (i) Calculate the distance moved by the car during this acceleration. distance = ............................................. m [2] (ii) The same force is used to change the speed of the car from 30 m s–1 to 45 m s–1. Explain why the distance moved is not the same as that calculated in (i). .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1]

Mark scheme: 2 (a) (i) force is rate of change of momentum B1 [1] (ii) work done is the product of the force and the distance moved in the direction of the force B1 [1] (b) (i) W = Fs or W = mas or W = m(v2 – u2) / 2 or W = force × distance s A1 [1] (ii) as = (v2 – u2) / 2 any subject M1 W = mas hence W = m(v2 – u2) / 2 M1 RHS represents terms of energy or with u = 0 KE = ½mv 2 A1 [3] (c) (i) work done = ½ × 1500 × [(30)2 – (15)2] (=506250) C1 distance = WD / F = 506250 / 3800 = 133 m A1 [2] or F = ma a = 2.533 (m s–2) C1 v2 = u2 + 2as s = 133 m A1 (ii) the change in kinetic energy is greater or the work done by the force has to be greater, hence distance is greater (for same force) A1 [1] allow: same acceleration, same time, so greater average speed and greater distance

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3 (a) Define For Examiner’s (i) stress, Use .................................................................................................................................. ..............................................................................................................................[1] (ii) strain. .................................................................................................................................. ..............................................................................................................................[1] (b) Explain the term elastic limit. .......................................................................................................................................... ......................................................................................................................................[1] (c) Explain the term ultimate tensile stress. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2] (d) (i) A ductile material in the form of a wire is stretched up to its breaking point. On Fig. 3.1, sketch the variation with extension x of the stretching force F. F 0 0 x Fig. 3.1 [2] (ii) On Fig. 3.2, sketch the variation with x of F for a brittle material up to its breaking For point. Examiner’s Use F 0 0 x Fig. 3.2 [1] (e) (i) Explain the features of the graphs in (d) that show the characteristics of ductile and brittle materials. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[2] (ii) The force F is removed from the materials in (d) just before the breaking point is reached. Describe the subsequent change in the extension for 1. the ductile material, .................................................................................................................................. ..............................................................................................................................[1] 2. the brittle material. .................................................................................................................................. ..............................................................................................................................[1]

Mark scheme: 3 (a) (i) stress = force / (cross-sectional) area B1 [1] (ii) strain = extension / original length or change in length / original length B1 [1] (b) point beyond which material does not return to the original length / shape / size when the load / force is removed B1 [1] GCE AS/A LEVEL – October/November 2011 9702 22 (c) UTS is the maximum force / original cross-sectional area M1 wire is able to support / before it breaks A1 [2] allow one: maximum stress the wire is able to support / before it breaks (d) (i) straight line from (0,0) M1 correct shape in plastic region A1 [2] (ii) only a straight line from (0,0) B1 [1] (e) (i) ductile: initially force proportional to extension then a large extension for small change in force B1 brittle: force proportional to extension until it breaks B1 [2] (ii) 1. does not return to its original length / permanent extension (as entered plastic region) B1 2. returns to original length / no extension (as no plastic region / still in elastic region) B1 [2]

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4 (a) Define electric field strength. For Examiner’s .......................................................................................................................................... Use ......................................................................................................................................[1] (b) Two horizontal metal plates are 20 mm apart in a vacuum. A potential difference of 1.5 kV is applied across the plates, as shown in Fig. 4.1. metal plate +1.5 kV oil drop 20 mm 0 V metal plate Fig. 4.1 A charged oil drop of mass 5.0 × 10–15 kg is held stationary by the electric field. (i) On Fig. 4.1, draw lines to represent the electric field between the plates. [2] (ii) Calculate the electric field strength between the plates. electric field strength = ....................................... V m–1 [1] (iii) Calculate the charge on the drop. charge = ............................................. C [4] (iv) The potential of the upper plate is increased. Describe and explain the subsequent motion of the drop. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[2]

Mark scheme: 4 (a) electric field strength = force / positive charge B1 [1] (b) (i) at least three equally spaced parallel vertical lines B1 direction down B1 [2] (ii) E = 1500 / 20 × 10–3 = 75000 V m–1 A1 [1] (iii) F = qE C1 (W = mg and) qE = mg C1 q = mg / E = 5 × 10–15 × 9.81 / 75000 = 6.5 × 10–19 C A1 negative charge A1 [4] (iv) F > mg or F now greater B1 drop will move upwards B1 [2]

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5 A potentiometer circuit that is used as a means of comparing potential differences is shown For in Fig. 5.1. Examiner’s Use E1 r1 R1 H G I1 metal wire B J F I2 I3 A C r2 D E2 Fig. 5.1 A cell of e.m.f. E1 and internal resistance r1 is connected in series with a resistor of resistance R1 and a uniform metal wire of total resistance R2. A second cell of e.m.f. E2 and internal resistance r2 is connected in series with a sensitive ammeter and is then connected across the wire at BJ. The connection at J is halfway along the wire. The current directions are shown on Fig. 5.1. (a) Use Kirchhoff’s laws to obtain the relation (i) between the currents I1, I2 and I3, ..............................................................................................................................[1] (ii) between E1, R1, R2, r1, I1 and I2 in loop HBJFGH, ..............................................................................................................................[1] (iii) between E1, E2, r1, r2, R1, R2, I1 and I3 in the loop HBCDJFGH. ..............................................................................................................................[2] (b) The connection at J is moved along the wire. Explain why the reading on the ammeter changes. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2]

Mark scheme: 5 (a) (i) І1 + І3 = І2 A1 [1] (ii) E1 = І2R2 + І1R2 + І1R1+ І1r1 A1 [1] 2 2 (iii) E1 – E2 B1 = –І3r2 + І1 (R1 + r1 + R2 / 2) B1 [2] (b) p.d. across BJ of wire changes / resistance of BJ changes B1 there is a difference in p.d across wire and p.d. across cell E2 B1 [2]

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6 (a) State the principle of superposition. For Examiner’s .......................................................................................................................................... Use .......................................................................................................................................... ......................................................................................................................................[2] (b) An arrangement that can be used to determine the speed of sound in air is shown in Fig. 6.1. S L microphone loudspeaker c.r.o. Fig. 6.1 Sound waves of constant frequency are emitted from the loudspeaker L and are reflected from a point S on a hard surface. The loudspeaker is moved away from S until a stationary wave is produced. Explain how sound waves from L give rise to a stationary wave between L and S. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2] (c) A microphone connected to a cathode ray oscilloscope (c.r.o.) is positioned between L and S as shown in Fig. 6.1. The trace obtained on the c.r.o. is shown in Fig. 6.2. 1 cm 1 cm Fig. 6.2 The time-base setting on the c.r.o. is 0.10 ms cm–1. (i) Calculate the frequency of the sound wave. For Examiner’s Use frequency = ............................................ Hz [2] (ii) The microphone is now moved towards S along the line LS. When the microphone is moved 6.7 cm, the trace seen on the c.r.o. varies from a maximum amplitude to a minimum and then back to a maximum. 1. Use the properties of stationary waves to explain these changes in amplitude. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1] 2. Calculate the speed of sound. speed of sound = ........................................ m s–1 [3] Please turn over for Question 7.

Mark scheme: 6 (a) waves overlap B1 (resultant) displacement is the sum of the displacements of each of the waves B1 [2] GCE AS/A LEVEL – October/November 2011 9702 22 (b) waves travelling in opposite directions overlap / incident and reflected waves overlap (allow superpose or interfere for overlap here) B1 waves have the same speed and frequency B1 [2] (c) (i) time period = 4 × 0.1 (ms) C1 f = 1 / T = 1 / 4 × 10–4 = 2500 Hz A1 [2] (ii) 1. the microphone is at an antinode and goes to a node and then an antinode / maximum amplitude at antinode and minimum amplitude at node B1 [1] 2. λ / 2 = 6.7 (cm) C1 v = fλ C1 v = 2500 × 13.4 × 10–2 = 335 m s–1 A1 [3] incorrect λ then can only score second mark

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7 (a) State the experimental observations that show radioactive decay is For Examiner’s (i) spontaneous, Use .................................................................................................................................. ..............................................................................................................................[1] (ii) random. .................................................................................................................................. ..............................................................................................................................[1] (b) On Fig. 7.1, complete the charge and mass of α-particles, β-particles and γ-radiation. Give example speeds of α-particles and γ-radiation emitted by a laboratory source. α-particle β-particle γ-radiation charge 0 mass 4u speed up to 0.99c Fig. 7.1 [3] (c) Explain the process by which α-particles lose energy when they pass through air. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2]

Mark scheme: 7 (a) (i) the half life / count rate / rate of decay / activity is the same no matter what external factors / environmental factors or two named factors such as temperature and pressure changes are applied B1 [1] (ii) the observations of the count rate / count rate / rate of decay / activity / radioactivity during decay shows variations / fluctuations B1 [1] (b) property α-particle β-particle γ-radiation charge (+)2e –e 0 mass 4u 9.11 × 10–31 kg 0 speed 0.01 to 0.1 c up to 0.99 c c one mark for each correct line B3 [3] (c) collision with molecules B1 causes ionisation (of the molecule) / electron is removed B1 [2]

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