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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level * 0 0 2 1 2 3 9 3 0 7 * PHYSICS 9702/42 Paper 4 A2 Structured…
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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level * 0 0 2 1 2 3 9 3 0 7 * PHYSICS 9702/42 Paper 4 A2 Structured Questions May/June 2012 2 hours 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. DO NOT WRITE IN ANY BARCODES. For Examiner’s Use Answer all questions. You may lose marks if you do not show your working or if you do not use 1 appropriate units. 2 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 3 question. 4 5 6 7 8 9 10 11 12 Total This document consists of 23 printed pages and 1 blank page. DC (NH/SW) 42210/4 © UCLES 2012 [Turn over 2 Data speed of light in free space, c = 3.00 × 10 8 m s –1 permeability of free space, μ0 = 4π × 10 –7 H m–1 permittivity of free space, ε0 = 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 × 10 23 mol –1 the Boltzmann constant, k = 1.38 × 10 –23 J K –1 gravitational constant, G = 6.67 × 10 –11 N m 2 kg –2 acceleration of free fall, g = 9.81 m s –2 © UCLES 2012 9702/42/M/J/12 3 Formulae uniformly accelerated motion, s = ut +  at 2 v 2 = u 2 + 2as work done on/by a gas, W = p ΔV Gm gravitational potential, φ =– r hydrostatic pressure, p = ρgh Nm 2 pressure of an ideal gas, p =  V c simple harmonic motion, a = – ω 2x velocity of particle in s.h.m., v = v0 cos ωt v = ± ω √⎯(x⎯ 0⎯ 2 ⎯ –⎯ x⎯ ⎯ 2⎯ ) Q electric potential, V = 4πε0r capacitors in series, 1/C = 1/C1 + 1/C2 + . . . capacitors in parallel, C = C1 + C2 + . . . energy of charged capacitor, W =  QV resistors in series, R = R1 + R2 + . . . resistors in parallel, 1/R = 1/R1 + 1/R2 + . . . alternating current/voltage, x = x0 sin ω t radioactive decay, x = x0 exp(– λt ) 0.693 decay constant, λ = t  © UCLES 2012 9702/42/M/J/12 [Turn over 4 Section A For Examiner’s Answer all the questions in the spaces provided. Use 1 (a) State Newton’s law of gravitation. .......................................................................................................................................... .......................................................................................................................................... ...................................................................................................................................... [2] (b) The Earth and the Moon may be considered to be isolated in space with their masses concentrated at their centres. The orbit of the Moon around the Earth is circular with a radius of 3.84 × 105 km. The period of the orbit is 27.3 days. Show that (i) the angular speed of the Moon in its orbit around the Earth is 2.66 × 10–6 rad s–1, [1] (ii) the mass of the Earth is 6.0 × 1024 kg. [2] © UCLES 2012 9702/42/M/J/12 5 (c) The mass of the Moon is 7.4 × 1022 kg. For Examiner’s (i) Using data from (b), determine the gravitational force between the Earth and the Use Moon. force = .............................................. N [2] (ii) Tidal action on the Earth’s surface causes the radius of the orbit of the Moon to increase by 4.0 cm each year. Use your answer in (i) to determine the change, in one year, of the gravitational potential energy of the Moon. Explain your working. energy change = ............................................... J [3] © UCLES 2012 9702/42/M/J/12 [Turn over 6 2 A ball of mass 37 g is held between two fixed points A and B by two stretched helical springs, For as shown in Fig. 2.1. Examiner’s Use ball mass 37 g A B Fig. 2.1 The ball oscillates along the line AB with simple harmonic motion of frequency 3.5 Hz and amplitude 2.8 cm. (a) Show that the total energy of the oscillations is 7.0 mJ. [2] (b) At two points in the oscillation of the ball, its kinetic energy is equal to the potential energy stored in the springs. Calculate the magnitude of the displacement at which this occurs. displacement = ............................................ cm [3] © UCLES 2012 9702/42/M/J/12 7 (c) On the axes of Fig. 2.2 and using your answers in (a) and (b), sketch a graph to show For the variation with displacement x of Examiner’s Use (i) the total energy of the system (label this line T), [1] (ii) the kinetic energy of the ball (label this line K), [2] (iii) the potential energy stored in the springs (label this line P). [2] 8 6 energy / mJ 4 2 0 –3 –2 –1 0 1 2 3 x / cm Fig. 2.2 (d) The arrangement in Fig. 2.1 is now rotated through 90° so that the line AB is vertical and the ball oscillates in a vertical plane. Suggest one form of energy, other than those in (c), that must be taken into consideration when plotting new graphs to show energy changes with displacement. ...................................................................................................................................... [1] © UCLES 2012 9702/42/M/J/12 [Turn over 8 BLANK PAGE © UCLES 2012 9702/42/M/J/12 9 3 (a) State what is meant by the internal energy of a system. For Examiner’s .......................................................................................................................................... Use .......................................................................................................................................... ...................................................................................................................................... [2] (b) State and explain qualitatively the change, if any, in the internal energy of the following systems: (i) a lump of ice at 0 °C melts to form liquid water at 0 °C, .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .............................................................................................................................. [3] (ii) a cylinder containing gas at constant volume is in sunlight so that its temperature rises from 25 °C to 35 °C. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .............................................................................................................................. [3] © UCLES 2012 9702/42/M/J/12 [Turn over 10 4 A charged point mass is situated in a vacuum. A proton travels directly towards the mass, as For illustrated in Fig. 4.1. Examiner’s Use charged proton point mass r Fig. 4.1 When the separation of the mass and the proton is r, the electric potential energy of the system is UP . The variation with r of the potential energy UP is shown in Fig. 4.2. r / cm 0 2 4 6 8 10 0 –10 UP / 10–26 J –20 –30 –40 –50 Fig. 4.2 © UCLES 2012 9702/42/M/J/12 11 (a) (i) Use Fig. 4.2 to state and explain whether the mass is charged positively or For negatively. Examiner’s Use .................................................................................................................................. .................................................................................................................................. .............................................................................................................................. [2] (ii) The gradient at a point on the graph of Fig. 4.2 is G. Show that the electric field strength E at this point due to the charged point mass is given by the expression Eq = G where q is the charge at this point. .................................................................................................................................. .................................................................................................................................. .............................................................................................................................. [2] (b) Use the expression in (a)(ii) and Fig. 4.2 to determine the electric field strength at a distance of 4.0 cm from the charged point mass. field strength = ........................................ V m–1 [4] © UCLES 2012 9702/42/M/J/12 [Turn over 12 5 (a) Define the tesla. For Examiner’s .......................................................................................................................................... Use .......................................................................................................................................... .......................................................................................................................................... ...................................................................................................................................... [3] (b) A horseshoe magnet is placed on a balance. A stiff metal wire is clamped horizontally between the poles, as illustrated in Fig. 5.1. horseshoe magnet stiff metal wire balance pan Fig. 5.1 The magnetic flux density in the space between the poles of the magnet is uniform and is zero outside this region. The length of the metal wire normal to the magnetic field is 6.4 cm. When a current in the wire is switched on, the reading on the balance increases by 2.4 g. The current in the wire is 5.6 A. (i) State and explain the direction of the force on the wire due to the current. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .............................................................................................................................. [3] © UCLES 2012 9702/42/M/J/12 13 (ii) Calculate the magnitude of the magnetic flux density between the poles of the For magnet. Examiner’s Use flux density = ...............................................T [2] (c) A low frequency alternating current is now passed through the wire in (b). The root-mean-square (r.m.s.) value of the current is 5.6 A. Describe quantitatively the variation of the reading seen on the balance. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ...................................................................................................................................... [2] © UCLES 2012 9702/42/M/J/12 [Turn over 14 6 (a) Describe the main principles of the determination of the charge on an oil drop by For Millikan’s experiment. You may draw a diagram if you wish. Examiner’s Use .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ...................................................................................................................................... [7] (b) In an experiment to determine the fundamental charge, values of charge on oil drops were found by a student to be as shown below. 3.2 × 10–19 C; 6.4 × 10–19 C; 16 × 10–19 C; 9.7 × 10–19 C; 12.8 × 10–19 C; 3.1 × 10–19 C; 6.3 × 10–19 C. State the value, to two significant figures, of the fundamental charge that is suggested by these values of charge on oil drops. fundamental charge = .............................................. C [1] © UCLES 2012 9702/42/M/J/12 15 7 The photoelectric effect may be represented by the equation For Examiner’s photon energy = work function energy + maximum kinetic energy of electron. Use (a) State what is meant by work function energy. .......................................................................................................................................... ...................................................................................................................................... [1] (b) The variation with frequency f of the maximum kinetic energy EK of photoelectrons emitted from the surface of sodium metal is shown in Fig. 7.1. 0.8 0.6 EK / eV 0.4 0.2 0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 14 f / 10 Hz Fig. 7.1 Use the gradient of the graph of Fig. 7.1 to determine a value for the Planck constant h. Show your working. h = ............................................. J s [2] © UCLES 2012 9702/42/M/J/12 [Turn over 16 (c) The sodium metal in (b) has a work function energy of 2.4 eV. The sodium is replaced by For calcium which has a work function energy of 2.9 eV. Examiner’s Use On Fig. 7.1, draw a line to show the variation with frequency f of the maximum kinetic energy EK of photoelectrons emitted from the surface of calcium. [3] © UCLES 2012 9702/42/M/J/12 17 8 The element strontium has at least 16 isotopes. One of these isotopes is strontium-89. This For isotope has a half-life of 52 days. Examiner’s Use (a) State what is meant by isotopes. .......................................................................................................................................... .......................................................................................................................................... ...................................................................................................................................... [2] (b) Calculate the probability per second of decay of a nucleus of strontium-89. probability = ............................................ s–1 [3] (c) A laboratory prepares a strontium-89 source. The activity of this source is measured 21 days after preparation of the source and is found to be 7.4 × 106 Bq. Determine, for the strontium-89 source at the time that it was prepared, (i) the activity, activity = ............................................ Bq [2] (ii) the mass of strontium-89. mass = ............................................... g [2] © UCLES 2012 9702/42/M/J/12 [Turn over 18 Section B For Examiner’s Answer all the questions in the spaces provided. Use 9 An operational amplifier (op-amp) may be used as part of the processing unit in an electronic sensor. (a) State four properties of an ideal operational amplifier. 1. ...................................................................................................................................... 2. ...................................................................................................................................... 3. ...................................................................................................................................... 4. ...................................................................................................................................... [4] (b) A comparator circuit incorporating an ideal op-amp is shown in Fig. 9.1. +5 V – + VIN –5 V VOUT Fig. 9.1 The variation with time t of the input potential VIN is shown in Fig. 9.2. 6 potential /V 4 2 VIN 0 t –2 –4 –6 Fig. 9.2 On the axes of Fig. 9.2, draw a graph to show the variation with time t of the output potential VOUT . [3] © UCLES 2012 9702/42/M/J/12 19 (c) The output potential VOUT is to be displayed using two light-emitting diodes (LEDs). A For diode emitting red light is to indicate when VOUT is positive and a diode emitting green Examiner’s light is to be used to indicate when VOUT is negative. Use Complete Fig. 9.3 to show the connections of the two LEDs to the output of the op-amp. Label each LED with the colour of light that it emits. VOUT Fig. 9.3 [3] © UCLES 2012 9702/42/M/J/12 [Turn over 20 10 (a) An aluminium block is placed near to a small source of X-ray radiation, as shown in For Fig. 10.1. Examiner’s Use aluminium block X-ray A B source Fig. 10.1 X-rays from the source are detected at point A and at point B. State two reasons why the intensity of the X-ray beam at point B is not as great as the intensity at point A. 1. ...................................................................................................................................... .......................................................................................................................................... 2. ...................................................................................................................................... .......................................................................................................................................... [2] (b) A cross-section through a model of a finger is shown in Fig. 10.2. 2.4 cm 1.1 cm bone C D A B soft tissue Fig. 10.2 The thickness of the model is 2.4 cm and that of the bone in the model is 1.1 cm. Parallel beams of X-rays are incident on the model in the directions AB and CD, as shown in Fig. 10.2. © UCLES 2012 9702/42/M/J/12 21 Data for the linear attenuation (absorption) coefficient μ for the bone and the soft tissue For in the model are given in Fig. 10.3. Examiner’s Use μ / cm–1 bone 3.00 soft tissue 0.27 Fig. 10.3 Calculate the ratio intensity of X-ray beam incident on the model intensity of X-ray beam emergent from the model for (i) the beam AB, ratio = .................................................. [2] (ii) the beam CD. ratio = .................................................. [2] (c) Use your answers in (b) to suggest why, for this model, an X-ray image with good contrast may be obtained. .......................................
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