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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level * 1 7 4 6 8 2 5 5 7 1 * PHYSICS 9702/41 Paper 4 A2 Structured…
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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level * 1 7 4 6 8 2 5 5 7 1 * PHYSICS 9702/41 Paper 4 A2 Structured Questions October/November 2010 1 hour 45 minutes 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. 3 The number of marks is given in brackets [ ] at the end of each question or part question. 4 5 6 7 8 9 10 11 12 Total This document consists of 24 printed pages. DC (LEO/SW) 23673/4 © UCLES 2010 [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 2010 9702/41/O/N/10 3 Formulae 1 uniformly accelerated motion, s = ut + 2 at 2 v 2 = u 2 + 2as work done on/by a gas, W = pV gravitational potential, φ = – Gm r hydrostatic pressure, p = ρgh 1 Nm 2 pressure of an ideal gas, p = 3 c V simple harmonic motion, a = – ω 2x velocity of particle in s.h.m., v = v0 cos ωt v = ± ω √⎯(x⎯ 02⎯ –⎯ x⎯ 2⎯ ) Q electric potential, V = 4πε0r capacitors in series, 1/C = 1/C1 + 1/C2 + . . . capacitors in parallel, C = C1 + C2 + . . . 1 energy of charged capacitor, W = 2 QV resistors in series, R = R1 + R2 + . . . resistors in parallel, 1/R = 1/R1 + 1/R2 + . . . alternating current/voltage, x = x0 sin ωt radioactive decay, x = x0 exp(– λt ) 0.693 decay constant, λ = t1 2 © UCLES 2010 9702/41/O/N/10 [Turn over 4 Section A For Examiner’s Answer all the questions in the spaces provided. Use 1 (a) Define gravitational field strength. .......................................................................................................................................... ...................................................................................................................................... [1] (b) An isolated star has radius R. The mass of the star may be considered to be a point mass at the centre of the star. The gravitational field strength at the surface of the star is gs. On Fig. 1.1, sketch a graph to show the variation of the gravitational field strength of the star with distance from its centre. You should consider distances in the range R to 4R. 1.0gs 0.8gs gravitational field strength 0.6gs 0.4gs 0.2gs 0 R 2R 3R 4R surface distance of star Fig. 1.1 [2] (c) The Earth and the Moon may be considered to be spheres that are isolated in space with their masses concentrated at their centres. The masses of the Earth and the Moon are 6.00 × 1024 kg and 7.40 × 1022 kg respectively. The radius of the Earth is RE and the separation of the centres of the Earth and the Moon is 60 RE, as illustrated in Fig. 1.2. RE Moon mass Earth 7.40 x 1022 kg mass 6.00 x 1024 kg 60 RE Fig. 1.2 (not to scale) © UCLES 2010 9702/41/O/N/10 5 (i) Explain why there is a point between the Earth and the Moon at which the For gravitational field strength is zero. Examiner’s Use .................................................................................................................................. .................................................................................................................................. .............................................................................................................................. [2] (ii) Determine the distance, in terms of RE, from the centre of the Earth at which the gravitational field strength is zero. distance = ...........................................RE [3] (iii) On the axes of Fig. 1.3, sketch a graph to show the variation of the gravitational field strength with position between the surface of the Earth and the surface of the Moon. gravitational field strength 0 surface surface distance of Earth of Moon Fig. 1.3 [3] © UCLES 2010 9702/41/O/N/10 [Turn over 6 2 (a) (i) State the basic assumption of the kinetic theory of gases that leads to the conclusion For that the potential energy between the atoms of an ideal gas is zero. Examiner’s Use .................................................................................................................................. .............................................................................................................................. [1] (ii) State what is meant by the internal energy of a substance. .................................................................................................................................. .................................................................................................................................. .............................................................................................................................. [2] (iii) Explain why an increase in internal energy of an ideal gas is directly related to a rise in temperature of the gas. .................................................................................................................................. .................................................................................................................................. .............................................................................................................................. [2] (b) A fixed mass of an ideal gas undergoes a cycle PQRP of changes as shown in Fig. 2.1. 10 8 P volume / 10–4 m3 6 4 2 Q R 0 0 5 10 15 20 25 30 pressure / 105 Pa Fig. 2.1 © UCLES 2010 9702/41/O/N/10 7 (i) State the change in internal energy of the gas during one complete cycle PQRP. For Examiner’s change = ............................................. J [1] Use (ii) Calculate the work done on the gas during the change from P to Q. work done = .............................................. J [2] (iii) Some energy changes during the cycle PQRP are shown in Fig. 2.2. work done on gas heating supplied increase in change /J to gas / J internal energy / J P Q ............................. –600 ............................. Q R 0 +720 ............................. R P ............................. +480 ............................. Fig. 2.2 Complete Fig. 2.2 to show all of the energy changes. [3] © UCLES 2010 9702/41/O/N/10 [Turn over 8 3 A student sets up the apparatus illustrated in Fig. 3.1 in order to investigate the oscillations of For a metal cube suspended on a spring. Examiner’s Use pulley variable-frequency oscillator thread spring metal cube Fig. 3.1 The amplitude of the vibrations produced by the oscillator is constant. The variation with frequency of the amplitude of the oscillations of the metal cube is shown in Fig. 3.2. 20 15 amplitude / mm 10 5 0 2 4 6 8 10 frequency / Hz Fig. 3.2 (a) (i) State the phenomenon illustrated in Fig. 3.2. .............................................................................................................................. [1] (ii) For the maximum amplitude of vibration, state the magnitudes of the amplitude and the frequency. amplitude = ............................................. mm frequency = ............................................... Hz [1] © UCLES 2010 9702/41/O/N/10 9 (b) The oscillations of the metal cube of mass 150 g may be assumed to be simple For harmonic. Examiner’s Use your answers in (a)(ii) to determine, for the metal cube, Use (i) its maximum acceleration, acceleration = ...................................... m s–2 [3] (ii) the maximum resultant force on the cube. force = .......................................... N [2] (c) Some very light feathers are attached to the top surface of the cube so that the feathers extend outwards, beyond the vertical sides of the cube. The investigation is now repeated. On Fig. 3.2, draw a line to show the new variation with frequency of the amplitude of vibration for frequencies between 2 Hz and 10 Hz. [2] © UCLES 2010 9702/41/O/N/10 [Turn over 10 4 (a) Define capacitance. For Examiner’s .......................................................................................................................................... Use ...................................................................................................................................... [1] (b) An isolated metal sphere has a radius r. When charged to a potential V, the charge on the sphere is q. The charge may be considered to act as a point charge at the centre of the sphere. (i) State an expression, in terms of r and q, for the potential V of the sphere. .............................................................................................................................. [1] (ii) This isolated sphere has capacitance. Use your answers in (a) and (b)(i) to show that the capacitance of the sphere is proportional to its radius. [1] (c) The sphere in (b) has a capacitance of 6.8 pF and is charged to a potential of 220 V. Calculate (i) the radius of the sphere, radius = ........................................... m [3] © UCLES 2010 9702/41/O/N/10 11 (ii) the charge, in coulomb, on the sphere. For Examiner’s Use charge = ........................................... C [1] (d) A second uncharged metal sphere is brought up to the sphere in (c) so that they touch. The combined capacitance of the two spheres is 18 pF. Calculate (i) the potential of the two spheres, potential = ............................................ V [1] (ii) the change in the total energy stored on the spheres when they touch. change = ........................................... J [3] © UCLES 2010 9702/41/O/N/10 [Turn over 12 5 Positive ions are travelling through a vacuum in a narrow beam. The ions enter a region of For uniform magnetic field of flux density B and are deflected in a semi-circular arc, as shown in Examiner’s Fig. 5.1. Use detector uniform magnetic field 12.8 cm beam of positive ions Fig. 5.1 The ions, travelling with speed 1.40 × 105 m s–1, are detected at a fixed detector when the diameter of the arc in the magnetic field is 12.8 cm. (a) By reference to Fig. 5.1, state the direction of the magnetic field. ...................................................................................................................................... [1] (b) The ions have mass 20 u and charge +1.6 × 10–19 C. Show that the magnetic flux density is 0.454 T. Explain your working. [3] © UCLES 2010 9702/41/O/N/10 13 (c) Ions of mass 22 u with the same charge and speed as those in (b) are also present in For the beam. Examiner’s Use (i) On Fig. 5.1, sketch the path of these ions in the magnetic field of magnetic flux density 0.454 T. [1] (ii) In order to detect these ions at the fixed detector, the magnetic flux density is changed. Calculate this new magnetic flux density. magnetic flux density = ............................................. T [2] © UCLES 2010 9702/41/O/N/10 [Turn over 14 6 A simple iron-cored transformer is illustrated in Fig. 6.1. For Examiner’s iron Use core input output primary secondary coil coil Fig. 6.1 (a) (i) State why the primary and secondary coils are wound on a core made of iron. .................................................................................................................................. .................................................................................................................................. .............................................................................................................................. [1] (ii) Suggest why thermal energy is generated in the core when the transformer is in use. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .............................................................................................................................. [3] © UCLES 2010 9702/41/O/N/10 15 (b) The root-mean-square (r.m.s.) voltage and current in the primary coil are VP and IP For respectively. Examiner’s The r.m.s. voltage and current in the secondary coil are VS and IS respectively. Use (i) Explain, by reference to direct current, what is meant by the root-mean-square value of an alternating current. .................................................................................................................................. .................................................................................................................................. .............................................................................................................................. [2] (ii) Show that, for an ideal transformer, VS IP = . VP IS [2] © UCLES 2010 9702/41/O/N/10 [Turn over 16 7 (a) State an effect, one in each case, that provides evidence for For Examiner’s (i) the wave nature of a particle, Use .............................................................................................................................. [1] (ii) the particulate nature of electromagnetic radiation. .............................................................................................................................. [1] (b) Four electron energy levels in an atom are shown in Fig. 7.1. –0.87 × 10–19 J –1.36 × 10–19 J electron energy –2.42 × 10–19 J –5.44 × 10–19 J Fig. 7.1 (not to scale) An emission spectrum is associated with the electron transitions between these energy levels. For this spectrum, (i) state the number of lines, .............................................................................................................................. [1] (ii) calculate the minimum wavelength. wavelength = ........................................... m [2] © UCLES 2010 9702/41/O/N/10 17 8 In some power stations, nuclear fission is used as a source of energy. For Examiner’s (a) State what is meant by nuclear fission. Use ......................................................................................................................................... .......................................................................................................................................... ...................................................................................................................................... [2] (b) The nuclear fission reaction produces neutrons. In the power station, the neutrons may be absorbed by rods made of boron-10. Complete the nuclear equation for the absorption of a single neutron by a boron-10 nucleus with the emission of an a-particle. 10 ....... 5B + ...................... 3Li + ...................... [3] (c) Suggest why, when neutrons are absorbed in the boron rods, the rods become hot as a result of this nuclear reaction. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ...................................................................................................................................... [3] © UCLES 2010 9702/41/O/N/10 [Turn over 18 Section B For Examiner’s Answer all the questions in the spaces provided. Use 9 An amplifier circuit incorporating an operational amplifier (op-amp) is shown in Fig. 9.1. R2 +9 V – + –9 V VOUT VIN R1 Fig. 9.1 (a) State (i) the name of this type of amplifier circuit, .............................................................................................................................. [1] (ii) the gain G in terms of resistances R1 and R2. .............................................................................................................................. [1] © UCLES 2010 9702/41/O/N/10 19 (b) The value of R1 is 820 Ω. The resistor of resistance R2 is replaced with a light-dependent For resistor (LDR). Examiner’s The input potential difference VIN is 15 mV. Use Calculate the output potential difference VOUT for the LDR having a resistance of (i) 100 Ω (the LDR is in sunlight), VOUT = ............................................. V [2] (ii) 1.0 MΩ (the LDR is in darkness). VOUT = ........................................... V [1] © UCLES 2010 9702/41/O/N/10 [Turn over 20 10 (a) (i) State what is meant by the acoustic impedance of a medium. For Examiner’s .................................................................................................................................. Use .............................................................................................................................. [1] (ii) Data for some media are given in Fig. 10.1. medium speed of ultrasound acoustic impedance / m s–1 / kg m–2 s–1 air 330 4.3 × 102 gel 1500 1.5 × 106 soft tissue 1600 1.6 × 106 bone 4100 7.0 × 106 Fig. 10.1 Use data from Fig. 10.1 to calculate a value for the density of bone. density = .................................... kg m–3 [1] (b) A parallel beam of ultrasound has intensity I. It is incident at right-angles to a boundary between two media, as shown in Fig. 10.2. boundary incident intensity I transmitted intensity IT reflected intensity IR acoustic impedance Z1 acoustic impedance Z2 Fig. 10.2 The media have acoustic impedances of Z1 and Z2. The transmitted intensity of the ultrasound beam is IT and the reflected intensity is IR. (i) State the relation between I, IT and IR. .............................................................................................................................. [1] © UCLES 2010 9702/41/O/N/10 21 (ii) The reflection coefficient a is given by the expression For Examiner’s Use (Z2 – Z1)2 a= . (Z2 + Z1)2 Use data from Fig. 10.1 to determine the reflection coefficient a for a boundary between 1. gel and soft tissue, a = .................................................. [2] 2. air and soft tissue. a = .................................................. [1] (c) By reference to your answers in (b)(ii), explain the use of a gel on the surface of skin during ultrasound diagnosis. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ...................................................................................................................................... [3] © UCLES 2010 9702/41/O/N/10 [Turn over 22 11 (a) Wire pairs provide one means of communication but they are subject to high levels of For
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