Cambridge A Level Physics 9702 — 2006 Oct/Nov Paper 2 · Variant 1

This document consists of 14 printed pages and 2 blank pages. SP (SJF3678/CG) S98413/3 © UCLES 2006 [Turn over UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Subsidiary Level and Advanced Level PHYSICS Paper 2 AS Structured Questions 9702/02 October/November 2006 1 hour Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. You may lose marks if you do not show your working or if you do not use appropriate units. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. DO NOT WRITE IN THE BARCODE. DO NOT WRITE IN THE GREY AREAS BETWEEN THE PAGES. For Examiner’s Use 1 2 3 4 5 6 7 Total

2 9702/02/O/N/06 Data speed of light in free space, c = 3.00 × 108 m s–1 permeability of free space,
0 = 4 × 10–7 H m–1 permittivity of free space, 0 = 8.85 × 10–12 F m–1 elementary charge, e = 1.60 × 10–19 C the Planck constant, h = 6.63 × 10–34 J s unified atomic mass constant, u = 1.66 × 10–27 kg rest mass of electron, me = 9.11 × 10–31 kg rest mass of proton, mp = 1.67 × 10–27 kg molar gas constant, R = 8.31 J K–1 mol–1 the Avogadro constant, NA = 6.02 × 1023 mol–1 the Boltzmann constant, k = 1.38 × 10–23 J K–1 gravitational constant, G = 6.67 × 10–11 N m2 kg–2 acceleration of free fall, g = 9.81 m s–2 © UCLES 2006

3 9702/02/O/N/06 [Turn over Formulae uniformly accelerated motion, s = ut +
 at 2 v2 = u2 + 2as work done on/by a gas, W = pV gravitational potential, φ = – simple harmonic motion, a = –
2x velocity of particle in s.h.m., v = v0 cos
t v = ±
√(x2 0 – x2) resistors in series, R = R1 + R2 + . . . resistors in parallel, 1/R = 1/R1 + 1/R2 + . . . electric potential, V = capacitors in series, 1/C = 1/C1 + 1/C2 + . . . capacitors in parallel, C = C1 + C2 + . . . energy of charged capacitor, W =
 QV alternating current/voltage, x = x0 sin
t hydrostatic pressure, p = qgh pressure of an ideal gas, p =
 <c2> radioactive decay, x = x0 exp(– t) decay constant,  = critical density of matter in the Universe, q0 = equation of continuity, Av = constant Bernoulli equation (simplified), p1 +
 qv2 1 = p2 +
 qv2 2 Stokes’ law, F = Arv Reynolds’ number, Re = drag force in turbulent flow, F = Br2qv2 qvr  3H0 2 8G 0.693 t
 Nm V Q 40r Gm r © UCLES 2006

4 9702/02/O/N/06 Answer all the questions in the spaces provided. 1 (a) Define what is meant by (i) work done, … … … [2] (ii) power. … … [1] (b) A force F is acting on a body that is moving with velocity v in the direction of the force. Derive an expression relating the power P dissipated by the force to F and v. [2] (c) A car of mass 1900 kg accelerates from rest to a speed of 27 m s–1 in 8.1 s. (i) Calculate the average rate at which kinetic energy is supplied to the car during the acceleration. rate = ………………………. W [2] For Examiner’s Use © UCLES 2006

5 9702/02/O/N/06 [Turn over (ii) The car engine provides power at a constant rate. Suggest and explain why the acceleration of the car is not constant. … … … [2] For Examiner’s Use © UCLES 2006

6 9702/02/O/N/06 2 A student investigates the speed of a trolley as it rolls down a slope, as illustrated in Fig. 2.1. Fig. 2.1 The speed v of the trolley is measured using a speed sensor for different values of the time t that the trolley has moved from rest down the slope. Fig. 2.2 shows the variation with t of v. Fig. 2.2 For Examiner’s Use © UCLES 2006 speed sensor trolley 0 0 0.5 1.0 1.5 2.0 0.2 0.4 0.6 0.8 1.0 t / s v / m s-1 1.2

7 9702/02/O/N/06 [Turn over (a) Use Fig. 2.2 to determine the acceleration of the trolley at the point on the graph where t = 0.80 s. acceleration = ………………………… m s–2 [4] (b) (i) State whether the acceleration is increasing or decreasing for values of t greater than 0.6 s. Justify your answer by reference to Fig. 2.2. … … … [2] (ii) Suggest an explanation for this change in acceleration. … … [1] (c) Name the feature of Fig. 2.2 that indicates the presence of (i) random error, … … [1] (ii) systematic error. … … [1] For Examiner’s Use © UCLES 2006

8 9702/02/O/N/06 3 Francium-208 is radioactive and emits α-particles with a kinetic energy of 1.07 ×10–12J to form nuclei of astatine, as illustrated in Fig. 3.1. Fig. 3.1 (a) State the nature of an α-particle. … … [1] (b) Show that the initial speed of an α-particle after the decay of a francium nucleus is approximately 1.8 ×107m s–1. [2] (c) (i) State the principle of conservation of linear momentum. … … … [2] For Examiner’s Use © UCLES 2006 francium nucleus before decay astatine nucleus - particle

9 9702/02/O/N/06 [Turn over (ii) The Francium-208 nucleus is stationary before the decay. Estimate the speed of the astatine nucleus immediately after the decay. speed = ………………………… m s–1 [3] (d) Close examination of the decay of the francium nucleus indicates that the astatine nucleus and the α-particle are not ejected exactly in opposite directions. Suggest an explanation for this observation. … … … [2] For Examiner’s Use © UCLES 2006

10 9702/02/O/N/06 4 (a) In order that interference between waves from two sources may be observed, the waves must be coherent. Explain what is meant by (i) interference, … … … [2] (ii) coherence. … … [1] (b) Red light of wavelength 644 nm is incident normally on a diffraction grating having 550 lines per millimetre, as illustrated in Fig. 4.1. Fig. 4.1 Red light of wavelength λ is also incident normally on the grating. The first order diffracted light of both wavelengths is illustrated in Fig. 4.1. For Examiner’s Use © UCLES 2006 incident light diffraction grating wavelengths 644 nm and 1st order, wavelength 644 nm 1st order, wavelength 1st order, wavelength 644 nm zero order 1st order, wavelength

11 9702/02/O/N/06 [Turn over (i) Calculate the number of orders of diffracted light of wavelength 644 nm that are visible on each side of the zero order. number = ………………………… [4] (ii) State and explain 1. whether λ is greater or smaller than 644 nm, … … [1] 2. in which order of diffracted light there is the greatest separation of the two wavelengths. … … … [2] . For Examiner’s Use © UCLES 2006

12 9702/02/O/N/06 5 (a) Distinguish between the structure of a metal and of a polymer. metal: … … … polymer: … … … [4] (b) Latex is a natural form of rubber. It is a polymeric material. (i) Describe the properties of a sample of latex. … … … [2] (ii) The process of heating latex with a small amount of sulphur creates cross-links between molecules. Natural latex has very few cross-links between its molecules. Suggest how this process changes the properties of latex. … … … [2] For Examiner’s Use © UCLES 2006

13 9702/02/O/N/06 [Turn over 6 A straight wire of unstretched length L has an electrical resistance R. When it is stretched by a force F, the wire extends by an amount ∆L and the resistance increases by ∆R. The area of cross-section A of the wire may be assumed to remain constant. (a) (i) State the relation between R, L, A and the resistivity ρ of the material of the wire. … … [1] (ii) Show that the fractional change in resistance is equal to the strain in the wire. [2] (b) A steel wire has area of cross-section 1.20 ×10–7m2 and a resistance of 4.17 Ω. The Young modulus of steel is 2.10 ×1011Pa. The tension in the wire is increased from zero to 72.0 N. The wire obeys Hooke’s law at these values of tension. Determine the strain in the wire and hence its change in resistance. Express your answer to an appropriate number of significant figures. change = ………………………… Ω[5] For Examiner’s Use © UCLES 2006 ∆R R

14 9702/02/O/N/06 7 (a) Distinguish between the electromotive force (e.m.f.) of a cell and the potential difference (p.d.) across a resistor. … … … … [3] (b) Fig. 7.1. is an electrical circuit containing two cells of e.m.f. E1 and E2. Fig. 7.1 The cells are connected to resistors of resistance R1, R2 and R3 and the currents in the branches of the circuit are I1, I2 and I3, as shown. (i) Use Kirchhoff’s first law to write down an expression relating I1, I2 and I3. … [1] (ii) Use Kirchhoff’s second law to write down an expression relating 1. E2, R2, R3, I2 and I3 in the loop XBCYX, … [1] 2. E1, E2, R1, R2, I1 and I2 in the loop AXYDA. … [1] For Examiner’s Use © UCLES 2006 E1 I1 I2 I3 E2 R1 R2 R3 A X B D Y C

16 9702/02/O/N/06 BLANK PAGE Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2006 question paper 9702 PHYSICS 9702/02 Paper 2 (Structured), maximum raw mark 60 This mark scheme is published as an aid to teachers and students, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began. All Examiners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes must be read in conjunction with the question papers and the report on the examination. The grade thresholds for various grades are published in the report on the examination for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 2006 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page 2 Mark Scheme Syllabus Paper GCE A/AS LEVEL - OCT/NOV 2006 9702 2 © UCLES 2006 1 (a) (i) product of force and distance moved M1 (by force) in the direction of the force A1 [2] (ii) work (done) per unit time (idea of ratio needed) B1 [1] (b) either work/time or power = (force × distance)/time M1 to give power = force × velocity A1 [2] (c) (i) kinetic energy (= ½mv2) = ½ × 1900 × 272 C1 power = 692550 / 8.1 = 8.55 × 104 W A1 [2] (ii) either for equal increments of speed, increments of EK are different M1 so longer time (to increase speed) at high speeds A1 [2] or air resistance increases with speed (M1) so driving force (and acceleration) reduced (A1) or P (= Fv) = mav (M1) (P and m constant) so when v increases, a decreases (A1) 2 (a) uses a tangent (anywhere), not a single point C1 draws tangent at correct position B1 acceleration = 1.7 ± 0.1 A2 [4] (outside 1.6 → 1.8 but within 1.5 → 1.9, allow 1 mark) (b) (i) because slope (of tangent of graph) is decreasing M1 acceleration is decreasing A1 [2] (ii) e.g. air resistance increases (with speed) (angle of) slope of ramp decreases B1 [1] (c) (i) scatter of points about line B1 [1] (ii) intercept / line does not go through origin B1 [1] 3 (a) helium nucleus OR contains two protons and two neutrons B1 [1] (b) kinetic energy = ½mv2 C1 ½ × 4 × 1.66 × 10-27 × v2 = 1.07 × 10-12 A1 v = 1.8 × 107 m s-1 A0 [2] (c) (i) sum of momenta (in any direction) is constant / total momemtum is constant M1 in a closed system / no external force A1 [2] (ii) momentum of francium (= 0) = momentum of α + momentum of astatine C1 204 × V = 4 × 1.8 × 107 C1 V = 3.5 × 105 m s-1 A1 [3] (nuclei incorrectly identified, 0/3 nuclei correctly identified but incorrect masses, -1 each error) (d) another particle / photon is emitted M1 at an angle to the direction of the α-particle A1 [2] (allow 1 mark for ‘Francium nucleus is not stationary’)

Page 3 Mark Scheme Syllabus Paper GCE A/AS LEVEL - OCT/NOV 2006 9702 2 © UCLES 2006 4 (a) (i) when two (or more) waves meet (at a point) M1 there is a change in overall intensity / displacement A1 (ii) constant phase difference (between waves) B1 [3] (b) (i) dsinθ = nλ B1 (10-3 / 550) sin90 = n × 644 × 10-9 C1 n = 2.8 C1 so two orders A1 [4] (power-of-ten error giving 2800 orders, allow 1/3 only for calculation of n) (ii) 1. dsinθ = nλ (either here or in (i) – not both) θ is greater so λ is greater B1 [1] 2. when n is larger, ∆θ is larger M1 so greater in second order A1 [2] 5 (a) metal: crystalline / lattice / atoms in regular pattern B1 (atoms in regular) pattern that repeats itself (within crystal) B1 [2] polymer: long chains of atoms / molecules B1 chain consists of ‘units’ that repeat themselves B1 [2] (b) (i) e.g. latex is soft / not strong / flows / ductile B1 elastic limit easily exceeded B1 [2] (allow any two sensible comments, 1 each) (ii) more solid / does not flow / stronger / higher ultimate tensile stress more brittle elastic limit much higher increased toughness (any two, 1 each) B2 [2] 6 (a) (i) R = ρL / A B1 (ii) strain = ∆L / L B1 either ∆R = ρ∆L /A or R ∝ L with ρ and A constant B1 dividing, ∆R / R = ∆L / L A0 [3] (b) Young modulus = stress / strain C1 strain = 72.0 / (1.20 × 10-7 × 2.10 × 1011) C1 = 2.86 × 10-3 (allow 1/350 A1 ∆R = 2.86 × 10-3 × 4.17 = 1.19 × 10-2 Ω A1 answer given to 3 sig. fig B1 [5] 7 (a) both measure (energy / work) / charge B1 for e.m.f., transfer of chemical energy to electrical energy B1 for p.d., transfer of electrical energy to thermal energy / other forms B1 [3] (b) (i) I1 + I2 = I3 B1 [1] (ii) 1. E2 = I2R2 + I3R3 B1 [1] 2. E1 - E2 = I1R1 - I2R2 B1 [1]