Cambridge A Level Physics 9702 — 2013 May/June Paper 2 · Variant 1

1 Energy is stored in a metal wire that is extended elastically. (a) Explain what is meant by extended elastically. .......................................................................................................................................... ..................................................................................................................................... [2] (b) Show that the SІ units of energy per unit volume are kg m–1 s–2. [2] (c) For a wire extended elastically, the elastic energy per unit volume X is given by X = Cε2E where C is a constant, ε is the strain of the wire, and E is the Young modulus of the wire. Show that C has no units. [3]

Mark scheme: 1 (a) the wire returns to its original length (not ‘shape’) M1 when the load is removed A1 [2] (b) energy: N m / kg m2 s–2 and volume m3 C1 energy / volume: kg m2 s–2 / m3 M1 energy / volume: kg m–1 s–2 A0 [2] (c) ε has no units B1 E: kg m s–2 m–2 M1 units of RHS: kg m–1 s–2 = LHS units / satisfactory conclusion to show C has no units A1 [3]

More questions on Stress and strain

2 (a) Distinguish between mass and weight. For Examiner’s mass: ............................................................................................................................... Use .......................................................................................................................................... weight: .............................................................................................................................. .......................................................................................................................................... [2] (b) An object O of mass 4.9 kg is suspended by a rope A that is fixed at point P. The object is pulled to one side and held in equilibrium by a second rope B, as shown in Fig. 2.1. P rope A Ƨ O rope B Fig. 2.1 Rope A is at an angle θ to the horizontal and rope B is horizontal. The tension in rope A is 69 N and the tension in rope B is T. (i) On Fig. 2.1, draw arrows to represent the directions of all the forces acting on object O. [2] (ii) Calculate For Examiner’s 1. the angle θ, Use θ = ................................................° [3] 2. the tension T. T = .............................................. N [2]

Mark scheme: 2 (a) mass is the property of a body resisting changes in motion / quantity of matter in a body / measure of inertia to changes in motion B1 weight is the force due to the gravitational field/force due to gravity or gravitational force B1 [2] Allow 1/2 for ‘mass is scalar weight is vector’ (b) (i) arrow vertically down through O B1 tension forces in correct direction on rope B1 [2] (ii) 1. weight = mg = 4.9 × 9.81 (= 48.07) C1 69 sin θ = mg C1 θ = 44.(1)° scale drawing allow ± 2° A1 [3] use of cos or tan 1/3 only 2. T = 69 cos θ C1 = 49.6 / 50 N scale drawing 50 ±2 (2/2) 50 ±4 (1/2) A1 [2] correct answers obtained using scale diagram or triangle of forces will score full marks cos in 1. then sin in 2. (2/2)

More questions on Momentum and Newton’s laws of motion

3 (a) An object falls vertically from rest through air. State and explain the energy conversions For that occur as the object falls. Examiner’s Use .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [3] (b) A ball of mass 150 g is thrown vertically upwards with an initial speed of 25 m s–1. (i) Calculate the initial kinetic energy of the ball. kinetic energy = .............................................. J [3] (ii) The ball reaches a height of 21 m above the point of release. For the ball rising to this height, calculate 1. the loss of energy of the ball to air resistance, energy loss = ............................................... J [3] 2. the average force due to the air resistance. force = .............................................. N [2]

Mark scheme: 3 (a) loss in potential energy due to decrease in height (as P.E. = mgh) (B1) gain in kinetic energy due to increase in speed (as K.E. = ½ mv2) (B1) special case ‘as PE decreases KE increases’ (1/2) increase in thermal energy due to work done against air resistance (B1) loss in P.E. equals gain in K.E. and thermal energy (B1) max. 3 [3] GCE AS/A LEVEL – May/June 2013 9702 21 (b) (i) kinetic energy = ½ mv2 C1 = ½ × 0.150 × (25)2 C1 = 46.875 = 47 J A1 [3] (ii) 1. potential energy (= mgh) = 0.150 × 9.81 × 21 C1 loss = KE – mgh = 46.875 – (30.9) C1 = 15.97 = 16 J A1 [3] 2. work done = 16 J work done = force × distance C1 F = 16 / 21 = 0.76 N A1 [2]

More questions on Gravitational potential energy and kinetic energy

4 (a) Define pressure. For Examiner’s .......................................................................................................................................... Use ..................................................................................................................................... [1] (b) Use the kinetic model to explain the pressure exerted by a gas. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [4] (c) Explain whether the collisions between the molecules of an ideal gas are elastic or inelastic. .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2]

Mark scheme: 4 (a) pressure = force / area (normal to force) A1 [1] (b) molecules/atoms/particles in (constant) random/haphazard motion B1 molecules have a change in momentum when they collide with the walls M1 (force exerted on molecules) therefore force on the walls A1 reference to average force from many molecules/many collisions A1 [4] (c) elastic collision when kinetic energy conserved B1 temperature constant for gas B1 [2]

More questions on Kinetic theory of gases

5 (a) State three conditions required for maxima to be formed in an interference pattern For produced by two sources of microwaves. Examiner’s Use 1. ...................................................................................................................................... .......................................................................................................................................... 2. ...................................................................................................................................... .......................................................................................................................................... 3. ...................................................................................................................................... .......................................................................................................................................... [3] (b) A microwave source M emits microwaves of frequency 12 GHz. Show that the wavelength of the microwaves is 0.025 m. [3] (c) Two slits S1 and S2 are placed in front of the microwave source M described in (b), as shown in Fig 5.1. P m 0.75 m S1 0.90 O M microwave detector S2 Fig. 5.1 (not to scale) The distances S1O and S2O are equal. A microwave detector is moved from O to P. The distance S1P is 0.75 m and the distance S2P is 0.90 m. The microwave detector gives a maximum reading at O. For Examiner’s State the variation in the readings on the microwave detector as it is moved slowly along Use the line from O to P. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [3] (d) The microwave source M is replaced by a source of coherent light. State two changes that must be made to the slits in Fig. 5.1 in order to observe an interference pattern. 1. ...................................................................................................................................... 2. ...................................................................................................................................... [2]

Mark scheme: 5 (a) waves overlap / meet / superpose (B1) coherence / constant phase difference (not constant λ or frequency) (B1) path difference = 0, λ, 2λ or phase difference = 0, 2π, 4π (B1) same direction of polarisation/unpolarised (B1) max. 3 [3] (b) λ = v / f C1 f = 12 × 109 Hz C1 λ = 3 × 108 / 12 × 109 (any subject) M1 = 0.025 m A0 [3] (c) maximum at P B1 several minima or maxima between O and P B1 5 maxima / 6 minima between O and P or 7 maxima / 6 minima including O and P B1 [3] (d) slits made narrower B1 slits put closer together B1 [2] (not just ‘make slits smaller’) Allow tilting the slits M1 and explanation of axes of rotation A1 GCE AS/A LEVEL – May/June 2013 9702 21

More questions on Interference

6 Two resistors A and B have resistances R1 and R2 respectively. The resistors are connected For in series with a battery, as shown in Fig. 6.1. Examiner’s Use E A B R1 R2 Fig. 6.1 The battery has electromotive force (e.m.f.) E and zero internal resistance. (a) State the energy transformation that occurs in (i) the battery, .................................................................................................................................. ............................................................................................................................. [1] (ii) the resistors. .................................................................................................................................. ............................................................................................................................. [1] (b) The current in the circuit is Ι. State the rate of energy transformation in (i) the battery, ............................................................................................................................. [1] (ii) the resistor A. ............................................................................................................................. [1] (c) The resistors are made from metal wires. Data for the resistors are given in Fig. 6.2. For Examiner’s Use resistor A B resistivity of metal ρ ρ / 2 length of wire l l diameter of wire d 2d Fig. 6.2 Use information from Fig. 6.2 to determine the ratio power dissipated in A . power dissipated in B ratio = .................................................. [3] (d) The resistors A and B are connected in parallel across the same battery of e.m.f. E. Determine the ratio power dissipated in A . power dissipated in B ratio = .................................................. [2]

Mark scheme: 6 (a) (i) chemical to electrical B1 [1] (ii) electrical to thermal / heat or heat and light B1 [1] (b) (i) (PB =) EI or I2(R1 + R2) A1 [1] (ii) (PR =) I2R1 A1 [1] (c) R = ρl / A or clear from the following equation B1 ρl / πd 2 ratio = I2R1 / I2R2 = 2 or R1 has 8 × resistance of R 2 C1 ρ (2l ) / π (2d ) = 8 or 8:1 A1 [3] (d) P = V2 / R or E2 / R C1 (V or E the same) hence ratio is 1/8 or 1:8 = 0.125 (allow ecf from (c)) A1 [2]

More questions on Potential difference and power

7 (a) Describe the two main results of the α-particle scattering experiment. For Examiner’s result 1: ............................................................................................................................ Use .......................................................................................................................................... result 2: ............................................................................................................................ .......................................................................................................................................... [3] (b) Relate each of the results in (a) with the conclusions that were made about the nature of atoms. result 1: ............................................................................................................................ .......................................................................................................................................... result 2: ............................................................................................................................ .......................................................................................................................................... [3]

Mark scheme: 7 (a) the majority/most went straight through or were deviated by small angles B1 a very small proportion/a few were deviated by large angles B1 small angles described as < 10° and large angles described as >90° B1 [3] (b) most of the atom is empty space/nucleus very small compared with atom B1 mass and charge concentrated in (very small) nucleus B1 correct links made with statements in (a) B1 [3]

More questions on Atoms, nuclei and radiation