Cambridge A Level Physics 9702 — 2006 May/June Paper 2 · Variant 1

1 (a) Derive the SI base unit of force. SI base unit of force = ………………………………… [1] (b) A spherical ball of radius r experiences a resistive force F due to the air as it moves through the air at speed v. The resistive force F is given by the expression F = crv, where c is a constant. Derive the SI base unit of the constant c. SI base unit of c = ………………………………… [1] Use (c) The ball is dropped from rest through a height of 4.5 m. (i) Assuming air resistance to be negligible, calculate the final speed of the ball. speed = …………………………… m s–1 [2] (ii) The ball has mass 15 g and radius 1.2 cm. The numerical value of the constant c in the equation in (b) is equal to 3.2 ×10–4 when measured using the SI system of units. Show quantitatively whether the assumption made in (i) is justified. [3]

Mark scheme: 1 (a) kg m s–2 B1 [1] (b) kg m–1 s–1 B1 [1] (c) (i) v2 = 2gs = 2 × 9.8 × 4.5 C1 v = 9.4 m s–1 A1 [2] (ii) either F (= 3.2 × 10–4 × 1.2 × 10–2 × 9.4) = 3.6 × 10–5 N M1 weight of sphere (= mg = 15 × 10–3 × 9.8) = 0.15 N M1 3.6 × 10–5 << 0.15, so justified A1 [3] or mg = crvT (M1) terminal speed = 3.8 × 104 m s–1 (M1) 9.4 << 3.8 × 104, so justified (A1)

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2 A rod AB is hinged to a wall at A. The rod is held horizontally by means of a cord BD, attached to the rod at end B and to the wall at D, as shown in Fig. 2.1. wall D cord T hinge P F C B A rod W Fig. 2.1 The rod has weight W and the centre of gravity of the rod is at C. The rod is held in equilibrium by a force T in the cord and a force F produced at the hinge. (a) Explain what is meant by (i) the centre of gravity of a body, ................................................................................................................................... ................................................................................................................................... .............................................................................................................................. [2] (ii) the equilibrium of a body. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... .............................................................................................................................. [2] Use (b) The line of action of the weight W of the rod passes through the cord at point P. Explain why, for the rod to be in equilibrium, the force F produced at the hinge must also pass through point P. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2] (c) The forces F and T make angles α and β respectively with the rod and AC = AB, as shown in Fig. 2.1. Write down equations, in terms of F, W, T, α and β, to represent (i) the resolution of forces horizontally, .............................................................................................................................. [1] (ii) the resolution of forces vertically, .............................................................................................................................. [1] (iii) the taking of moments about A. .............................................................................................................................. [1]

Mark scheme: 2 (a) (i) point at which whole weight of body M1 may be considered to act A1 [2] (ii) sum of forces in any direction is zero B1 sum of moments about any point is zero B1 [2] (b) either: T and W have zero moment about P M1 so F must have zero moment, i.e. pass through P A1 [2] or: if all pass through P, distance from P is zero for all forces (M1) so sum of moments about P is zero (A1) (c) (i) Fcosα = Tcosβ B1 [1] (ii) W = Fsinα + Tsinβ B1 [1] (iii) 2W = 3Tsinβ B1 [1]

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3 (a) Explain what is meant by the internal energy of a substance. .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2] (b) State and explain, in molecular terms, whether the internal energy of the following increases, decreases or does not change. (i) a lump of iron as it is cooled ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... .............................................................................................................................. [3] (ii) some water as it evaporates at constant temperature ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... .............................................................................................................................. [3]

Mark scheme: 3 (a) sum of (random) kinetic and potential energies M1 of the atoms/molecules of the substance A1 [2] (b) (i) potential energy unchanged as atoms remain in same positions M1 allow ‘reduced because atoms slightly closer together’ vibrational kinetic energy reduced because temperature lower M1 so internal energy less A1 [3] (ii) potential energy increases because separation increases M1 kinetic energy unchanged because temperature unchanged M1 so internal energy increases A1 [3]

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4 (a) Define density. .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [1] (b) A U-tube contains some mercury. Water is poured into one arm of the U-tube and oil is poured into the other arm, as shown in Fig. 4.1. oil water 71 cm 53 cm mercury Fig. 4.1 The amounts of oil and water are adjusted until the surface of the mercury in the two arms is at the same horizontal level. (i) State how it is known that the pressure at the base of the column of water is the same as the pressure at the base of the column of oil. ................................................................................................................................... .............................................................................................................................. [1] (ii) The column of water, density 1.0 × 103kg m–3, is 53 cm high. The column of oil is 71 cm high. Calculate the density of the oil. Explain your working. density = ………………………………. kg m–3 [3]

Mark scheme: 4 (a) mass per unit volume (ratio idea must be clear, not units) B1 [1] (b) (i) pressure is same at the surface of mercury because at same horizontal level B1 [1] (ii) hρg is same for both B1 53 × 10–2 × 1.0 × 103 × g = 71 × 10–2 × ρ × g C1 ρ = 7.5 × 102 kg m–3 A1 [3] GCE A Level – May/June 2006 9702 02

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5 Fig. 5.1 shows the variation with force F of the extension x of a spring as the force is increased to F3 and then decreased to zero. F3 F F2 F1 0 0 x1 x2 x Fig. 5.1 (a) State, with a reason, whether the spring is undergoing an elastic change. .......................................................................................................................................... ..................................................................................................................................... [1] (b) The extension of the spring is increased from x1 to x2. Show that the work W done in extending the spring is given by W = k(x22 – x12), where k is the spring constant. [3] Use (c) A trolley of mass 850 g is held between two fixed points by means of identical springs, as shown in Fig. 5.2. trolley spring Fig. 5.2 When the trolley is in equilibrium, the springs are each extended by 4.5 cm. Each spring has a spring constant 16 N cm–1. The trolley is moved a distance of 1.5 cm along the direction of the springs. This causes the extension of one spring to be increased and the extension of the other spring to be decreased. The trolley is then released. The trolley accelerates and reaches its maximum speed at the equilibrium position. Assuming that the springs obey Hooke’s law, use the expression in (b) to determine the maximum speed of the trolley. speed = …………………………. m s–1 [4]

Mark scheme: 5 (a) no hysteresis loop/no permanent deformation M1 (do not allow ‘force proportional to extension’) so elastic change A0 [1] (b) work done = area under graph line OR average force × distance B1 = ½Fx ½(F2 + F1)(x2 – x1) A1 F = kx, so work done = = ½kx2 ½k(x2 + x1)(x2 – x1) A1 work done = ½k(x22 – x12) A0 [3] (c) gain in energy of trolley = ½k(0.0602 – 0.0452) + ½k(0.0302 – 0.0452) C1 = 0.36 J C1 kinetic energy = ½ × 0.85 × v2 = 0.36 C1 v = 0.92 m s–1 A1 [4]

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6 A long tube, fitted with a tap, is filled with water. A tuning fork is sounded above the top of the tube as the water is allowed to run out of the tube, as shown in Fig. 6.1. tuning fork 512 Hz 32.4 cm Fig. 6.1 Fig. 6.2 A loud sound is first heard when the water level is as shown in Fig. 6.1, and then again when the water level is as shown in Fig. 6.2. Fig. 6.1 illustrates the stationary wave produced in the tube. (a) On Fig. 6.2, (i) sketch the form of the stationary wave set up in the tube, [1] (ii) mark, with the letter N, the positions of any nodes of the stationary wave. [1] Use (b) The frequency of the fork is 512 Hz and the difference in the height of the water level for the two positions where a loud sound is heard is 32.4 cm. Calculate the speed of sound in the tube. speed = …………………… m s–1 [3] (c) The length of the column of air in the tube in Fig. 6.1 is 15.7 cm. Suggest where the antinode of the stationary wave produced in the tube in Fig. 6.1 is likely to be found. .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2]

Mark scheme: 6 (a) (i) correct shape drawn B1 [1] (ii) two nodes marked correctly B1 [1] (b) ½λ = 0.324 m C1 v = fλ C1 = 512 × 2 × 0.324 = 332 m s–1 A1 [3] (c) ¼λ = 16.2 cm C1 either antinode is 0.5 cm above top of tube or antinode is 16.2 cm above water surface A1 [2]

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7 A circuit contains three similar lamps A, B and C. The circuit also contains three switches, S1, S2 and S3, as shown in Fig. 7.1. A X S1 S2 S3 B C Y Fig. 7.1 One of the lamps is faulty. In order to detect the fault, an ohm-meter (a meter that measures resistance) is connected between terminals X and Y. When measuring resistance, the ohm- meter causes negligible current in the circuit. Fig. 7.2 shows the readings of the ohm-meter for different switch positions. switch meter reading S1 S2 S3 / Ω open open open ∞ closed open open 15 Ω open closed open 30 Ω open closed closed 15 Ω Fig. 7.2 (a) Identify the faulty lamp, and the nature of the fault. faulty lamp: ....................................................................................................................... nature of fault: ............................................................................................................. [2] (b) Suggest why it is advisable to test the circuit using an ohm-meter that causes negligible current rather than with a power supply. .......................................................................................................................................... ..................................................................................................................................... [1] Use (c) Determine the resistance of one of the non-faulty lamps, as measured using the ohm- meter. resistance = …………………… Ω[1] (d) Each lamp is marked 6.0 V, 0.20 A. Calculate, for one of the lamps operating at normal brightness, (i) its resistance, resistance = …………………… Ω[2] (ii) its power dissipation. power = …………………… W [2] (e) Comment on your answers to (c) and (d)(i). .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2]

Mark scheme: 7 (a) lamp C M1 lamp is shorted A1 [2] (b) shorted lamp A would cause damage to the supply/lamps /blow fuse in supply B1 [1] (c) 15 Ω B1 [1] (d) (i) V = I R C1 R = 30 Ω A1 [2] (ii) P = VI or I2R or V2 / R C1 P = 1.2 W A1 [2] (e) filament is cold when measuring with ohm-meter in (b) B1 resistance of filament rises as temperature rises B1 [2]

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8 The radioactive decay of nuclei is both spontaneous and random. Explain what is meant by (a) radioactive decay of a nucleus, .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2] (b) spontaneous decay, .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2] (c) random decay. .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [2]

Mark scheme: 8 (a) nucleus emits M1 α- or β- particles and/or γ-rays A1 [2] (b) decay unaffected by environmental changes M1 such as temperature, pressure etc. (one e.g. is sufficient) A1 [2] (c) constant probability of decay (per unit time) of a nucleus B1 cannot predict which particular nucleus will decay next B1 [2]

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