Cambridge A Level Physics 9702 — 2017 May/June Paper 2 · Variant 1

1 (a) Determine the SI base units of stress. Show your working. base units ...........................................................[2] (b) A beam PQ is clamped so that the beam is horizontal. A mass M of 500 g is hung from end Q and the beam bends slightly, as illustrated in Fig. 1.1. clamp R l horizontal P Q M Fig. 1.1 The length l of the beam from the edge of the clamp R to end Q is 60.0 cm. The width b of the beam is 30.0 mm and the thickness d of the beam is 5.00 mm. The material of the beam has Young modulus E. The mass M is made to oscillate vertically. The time period T of the oscillations is 0.58 s. The period T is given by the expression 4 Ml 3 T = 2π 3 . Ebd (i) Determine E in GPa. E = ...................................................GPa [3] (ii) The quantities used to determine E should be measured with accuracy and with precision. 1. Explain the difference between accuracy and precision. accuracy: .................................................................................................................... ..................................................................................................................................... precision: .................................................................................................................... ..................................................................................................................................... [2] 2. In a particular experiment, the quantities l and T are measured with the same percentage uncertainty. State and explain which of these two quantities contributes more to the uncertainty in the value of E. ..................................................................................................................................... ..................................................................................................................................... .................................................................................................................................[1] [Total: 8]

Mark scheme: 1(a) B1 = kg m–1 s–2 A1 1(b)(i) 0.58 = 2π × [(4 × 0.500 × 0.6003 ) / (E × 0.0300 × 0.005003)]0.5 C1 E = [4π2 × 4 × 0.500 × (0.600)3] / [(0.58)2 × 0.0300 × (0.00500)3] = 1.35 × 1010 (Pa) C1 = 14 (13.5) GPa A1 1(b)(ii)1. (accuracy determined by) the closeness of the value(s)/measurement(s) to the true value B1 (precision determined by) the range of the values/measurements B1 1(b)(ii)2. l is (cubed so) 3 × (percentage/fractional) uncertainty and T is (squared so) 2 × (percentage / fractional) uncertainty and (so) l contributes more B1

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2 (a) State the two conditions for a system to be in equilibrium. 1. ............................................................................................................................................... ................................................................................................................................................... 2. ............................................................................................................................................... ................................................................................................................................................... [2] (b) A paraglider P of mass 95 kg is pulled by a wire attached to a boat, as shown in Fig. 2.1. parachute paraglider P wire boat horizontal 25° water Fig. 2.1 The wire makes an angle of 25° with the horizontal water surface. P moves in a straight line parallel to the surface of the water. The variation with time t of the velocity v of P is shown in Fig. 2.2. 10.0 8.0 v / m s–1 6.0 4.0 2.0 0 0 2.0 4.0 6.0 8.0 t / s Fig. 2.2 (i) Show that the acceleration of P is 1.4 m s–2 at time t = 5.0 s. [2] (ii) Calculate the total distance moved by P from time t = 0 to t = 7.0 s. distance = .......................................................m [2] (iii) Calculate the change in kinetic energy of P from time t = 0 to t = 7.0 s. change in kinetic energy = ........................................................J [2] (iv) The tension in the wire at time t = 5.0 s is 280 N. Calculate, for the horizontal motion, 1. the vertical lift force F supporting P, F = ....................................................... N [3] 2. the force R due to air resistance acting on P in the horizontal direction. R = ....................................................... N [3] [Total: 14]

Mark scheme: 2(a) resultant force (in any direction) is zero B1 resultant torque/moment (about any point) is zero B1 2(b)(i) a = (v − u) / t or gradient or ∆v / (∆)t C1 e.g. a = (8.8 − 4.6) / (7.0 – 4.0) = 1.4 m s–2 A1 2(b)(ii) s = 4.6 × 4 + [(8.8 + 4.6) / 2] × 3 C1 = 18.4 + 20.1 = 39 (38.5) m A1 2(b)(iii) ∆E = ½ × 95 [(8.8)2 − (4.6)2] C1 = 3678 – 1005 = 2700 (2673) J A1 2(b)(iv)1. weight = 95 × 9.81 (= 932 N) C1 vertical tension force = 280 sin 25° or 280 cos 65° (=118.3 N) C1 F = 932 + 118 = 1100 (1050) N A1 2(b)(iv)2. horizontal tension force = 280 cos 25° or 280 sin 65° (= 253.8 N) C1 resultant force = 95 × 1.4 (= 133 N) C1 133 = 253.8 – R R = 120 (120.8) N A1

More questions on Equations of motion

3 (a) A cylinder is made from a material of density 2.7 g cm–3. The cylinder has diameter 2.4 cm and length 5.0 cm. Show that the cylinder has weight 0.60 N. [3] (b) The cylinder in (a) is hung from the end A of a non-uniform bar AB, as shown in Fig. 3.1. 50 cm 20 cm bar 12 cm A B P X cylinder 0.25 N 0.60 N Fig. 3.1 The bar has length 50 cm and has weight 0.25 N. The centre of gravity of the bar is 20 cm from B. The bar is pivoted at P. The pivot is 12 cm from B. An object X is hung from end B. The weight of X is adjusted until the bar is horizontal and in equilibrium. (i) Explain what is meant by centre of gravity. ........................................................................................................................................... .......................................................................................................................................[1] (ii) Calculate the weight of X. weight of X = ............................................... N [3] (c) The cylinder is now immersed in water, as illustrated in Fig. 3.2. A B P water X 0.25 N Fig. 3.2 An upthrust acts on the cylinder and the bar is not in equilibrium. (i) Explain the origin of the upthrust. ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[2] (ii) Explain why the weight of X must be reduced in order to obtain equilibrium for AB. ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[1] [Total: 10]

Mark scheme: 3(a) C1 V = πd2L / 4 or πr2L C1 weight = 2.7 × 103 × π (1.2 × 10–2)2 × 5.0 × 10–2 × 9.81 = 0.60 N A1 3(b)(i) the point from where (all) the weight (of a body) seems to act B1 3(b)(ii) W × 12 C1 (0.25 × 8) + (0.6 × 38) C1 W = (2 + 22.8) / 12 = 2.1 (2.07) N A1 3(c)(i) pressure changes with depth (in water) or pressure on bottom (of cylinder) different from pressure on top B1 pressure on bottom of cylinder greater than pressure on top or force (up) on bottom of cylinder greater than force (down) on top B1 3(c)(ii) anticlockwise moment reduced and reducing the weight of X reduces clockwise moment or anticlockwise moment reduced so clockwise moment now greater than (total) anticlockwise moment B1

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4 (a) State the conditions required for the formation of stationary waves. ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[2] (b) One end of a string is attached to a vibrator. The string is stretched by passing the other end over a pulley and attaching a load, as illustrated in Fig. 4.1. string pulley A B vibrator support for pulley load Fig. 4.1 The frequency of vibration of the vibrator is adjusted to 250 Hz and a transverse wave travels along the string with a speed of 12 m s–1. The wave is reflected at the pulley and a stationary wave forms on the string. Fig. 4.2 shows the string between points A and B at time t = t1. string A B Fig. 4.2 At time t = t1 the string has maximum displacement. (i) Calculate the distance AB. distance = .......................................................m [2] (ii) On Fig. 4.2, sketch the position of the string between A and B at times 1. t = t1 + 2.0 ms (label this line P), 2. t = t1 + 5.0 ms (label this line Q). [3] [Total: 7]

Mark scheme: 4(a) (two) waves travelling (at same speed) in opposite directions overlap B1 waves (are same type and) have same frequency/wavelength B1 4(b)(i) λ = 12 / 250 (= 0.048 m) C1 distance = 1.5 × 0.048 = 0.072 m A1 4(b)(ii) T = 1 / 250 = 0.004 (s) or 4 (ms) C1 1. curve drawn is mirror image of that in Fig. 4.2 and labelled P A1 2. horizontal line drawn between A and B and labelled Q A1

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5 (a) Describe the Doppler effect. ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[1] (b) A car travels with a constant velocity along a straight road. The car horn with a frequency of 400 Hz is sounded continuously. A stationary observer on the roadside hears the sound from the horn at a frequency of 360 Hz. The speed of sound is 340 m s–1. Determine the magnitude v, and the direction, of the velocity of the car relative to the observer. v = .......................................................m s–1 direction ............................................................... [3] [Total: 4]

Mark scheme: 5(a) observed frequency is different to source frequency when source moves relative to observer B1 5(b) 360 = (400 × 340) / (340 ± v) C1 v = 38 (37.8) m s–1 A1 away (from the observer) B1

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6 (a) Define the ohm. ................................................................................................................................................... ...............................................................................................................................................[1] (b) A cell X of electromotive force (e.m.f.) 1.5 V and negligible internal resistance is connected in series to three resistors A, B and C, as shown in Fig. 6.1. X 1.5 V A 6.0 Ω C Ω B 4.0 3.0 Ω Fig. 6.1 Resistors A and B have resistances 6.0 Ω and 3.0 Ω respectively and are connected in parallel. Resistor C has resistance 4.0 Ω and is connected in series with the parallel combination. Calculate (i) the current in the circuit, current = ........................................................A [3] (ii) the current in resistor B, current = ........................................................A [1] (iii) the ratio power dissipated in resistor B . power dissipated in resistor C ratio = ...........................................................[2] (c) The resistors A, B and C in (b) are wires of the same material and have the same length. (i) Explain how the resistors may be made with different resistance values. .......................................................................................................................................[1] (ii) Calculate the ratio average drift speed of the charge carriers in resistor B . average drift speed of the charge carriers in resistor C ratio = ...........................................................[2] (d) A cell of e.m.f. 1.5 V and negligible internal resistance is connected in parallel with cell X in Fig. 6.1 with their positive terminals together. State the change, if any, to the current in (i) cell X, .......................................................................................................................................[1] (ii) resistor C. .......................................................................................................................................[1] [Total: 12]

Mark scheme: 6(a) volt / ampere B1 6(b)(i) RT = [1 / 3.0 + 1 / 6.0]–1 + 4.0 (= 6.0 Ω) C1 Ι = 1.5 / 6.0 C1 = 0.25 A A1 6(b)(ii) VB = 0.5 V I = 0.5 / 3.0 = 0.17 (0.167) A A1 6(b)(iii) P = I 2R or VI or V 2 / R C1 ratio = (0.1672 × 3.0) / (0.252 × 4.0) = 0.33 A1 6(c)(i) vary/change/different radius/diameter/cross-sectional area (of wire) B1 6(c)(ii) v = I / Ane ( ) ( ) = B C / ratio / A A B C I I or × C B A A B C I I C1 (R ∝ 1 / A so) ratio = × B C R R B C I I = × 0.167 3.0 0.25 4.0 = 0.50 A1 6(d)(i) 0.25 A to 0.13 (0.125) A or halved A1 6(d)(ii) no change A1

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7 (a) Use the quark model to show that (i) the charge on a proton is +e, .......................................................................................................................................[1] (ii) the charge on a neutron is zero. .......................................................................................................................................[1] (b) A nucleus of 9308Sr decays by the emission of a β– particle. A nucleus of 6249Cu decays by the emission of a β+ particle. (i) In Fig. 7.1, state the nucleon number and proton number for the nucleus produced in each of these decay processes. nucleus formed by β– decay nucleus formed by β+ decay nucleon number proton number Fig. 7.1 [1] (ii) State the name of the force responsible for β decay. .......................................................................................................................................[1] (iii) State the names of the leptons produced in each of the decay processes. β– decay: ........................................................................................................................... β+ decay: ............................................................................................................................ [1] [Total: 5]

Mark scheme: 7(a)(i) (proton is uud so) (2 / 3)e + (2 / 3)e – (1 / 3)e = e B1 7(a)(ii) (neutron is udd so) (2 / 3)e – (1 / 3)e –(1 / 3)e = 0 B1 7(b)(i) β– β+ nucleon number 90 64 proton number 39 28 all correct B1 7(b)(ii) weak (nuclear force/interaction) B1 7(b)(iii) β– decay: electron and (electron) antineutrino β+ decay: positron and (electron) neutrino all correct B1

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