UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level

Transcript

1 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level * * PHYSICS 9702/41 Paper 4 A2 Structured Questions May/June 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. Answer all questions. You may lose marks if you do not show your working or if you do not use appropriate units. 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 question Total This document consists of 21 printed pages and 3 blank pages. DC (LEO/CGW) 15337/4 [Turn over

2 2 Data speed of light in free space, c = ms 1 permeability of free space, μ 0 = 4π 10 7 Hm 1 permittivity of free space, ε 0 = Fm 1 elementary charge, the Planck constant, unified atomic mass constant, rest mass of electron, rest mass of proton, e = C h = Js u = kg m e = kg m p = kg molar gas constant, R = 8.31 J K 1 mol 1 the Avogadro constant, N A = mol 1 the Boltzmann constant, k = JK 1 gravitational constant, G = Nm 2 kg 2 acceleration of free fall, g = 9.81 m s /41/M/J/10

3 3 mulae uniformly accelerated motion, s = ut + at 2 v 2 = u 2 + 2as work done on/by a gas, W = p V gravitational potential, hydrostatic pressure, φ = Gm r p = ρgh pressure of an ideal gas, p = Nm V <c 2 > simple harmonic motion, velocity of particle in s.h.m., a = ω 2 x v = v 0 cos ωt v = ± ω (x 2 0 x 2 ) electric potential, Q V = 4πε 0 r capacitors in series, 1/C = 1/C 1 + 1/C capacitors in parallel, C = C 1 + C energy of charged capacitor, W = QV resistors in series, R = R 1 + R resistors in parallel, 1/R = 1/R 1 + 1/R alternating current/voltage, x = x 0 sin ωt radioactive decay, x = x 0 exp( λt) decay constant, λ = t 9702/41/M/J/10 [Turn over

4 4 Section A Answer all the questions in the spaces provided. 1 (a) Define the radian [2] (b) A stone of weight 3.0 N is fixed, using glue, to one end P of a rigid rod CP, as shown in Fig glue 85 cm P ω C stone, weight 3.0 N Fig. 1.1 The rod is rotated about end C so that the stone moves in a vertical circle of radius 85 cm. The angular speed ω of the rod and stone is gradually increased from zero until the glue snaps. The glue fixing the stone snaps when the tension in it is 18 N. the position of the stone at which the glue snaps, (i) on the dotted circle of Fig. 1.1, mark with the letter S the position of the stone, [1] (ii) calculate the angular speed ω of the stone. angular speed =... rad s 1 [4] 9702/41/M/J/10

5 5 2 (a) Some gas, initially at a temperature of 27.2 C, is heated so that its temperature rises to 38.8 C. Calculate, in kelvin, to an appropriate number of decimal places, (i) the initial temperature of the gas, initial temperature =... K [2] (ii) the rise in temperature. rise in temperature =... K [1] (b) The pressure p of an ideal gas is given by the expression p = 1 3 ρ c 2 where ρ is the density of the gas. (i) State the meaning of the symbol c 2....[1] (ii) the expression to show that the mean kinetic energy <E K > of the atoms of an ideal gas is given by the expression <E K > = 3 2 kt. Explain any symbols that you use.... [4] 9702/41/M/J/10 [Turn over

6 6 (c) Helium-4 may be assumed to behave as an ideal gas. A cylinder has a constant volume of cm 3 and contains helium-4 gas at a pressure of Pa and at a temperature of 290 K. Calculate, for the helium gas, (i) the amount of gas, amount =... mol [2] (ii) the mean kinetic energy of the atoms, mean kinetic energy =... J [2] (iii) the total internal energy. internal energy =... J [3] 9702/41/M/J/10

7 7 3 (a) State what is meant by (i) oscillations,...[1] (ii) free oscillations,...[1] (iii) simple harmonic motion....[2] (b) Two inclined planes RA and LA each have the same constant gradient. They meet at their lower edges, as shown in Fig ball L R A Fig. 3.1 A small ball moves from rest down plane RA and then rises up plane LA. It then moves down plane LA and rises up plane RA to its original height. The motion repeats itself. State and explain whether the motion of the ball is simple harmonic [2] 9702/41/M/J/10 [Turn over

8 8 4 (a) Explain what is meant by the potential energy of a body [2] (b) Two deuterium ( 2 1 H) nuclei each have initial kinetic energy E K and are initially separated by a large distance. The nuclei may be considered to be spheres of diameter m with their masses and charges concentrated at their centres. The nuclei move from their initial positions to their final position of just touching, as illustrated in Fig initially 2 1H 1H 2 kinetic energy E K kinetic energy E K m finally 2 1 H 2 1 H at rest Fig. 4.1 (i) the two nuclei approaching each other, calculate the total change in 1. gravitational potential energy, energy =... J [3] 2. electric potential energy. energy =... J [3] 9702/41/M/J/10

9 (ii) 9 your answers in (i) to show that the initial kinetic energy E K of each nucleus is 0.19 MeV. (iii) The two nuclei may rebound from each other. Suggest one other effect that could happen to the two nuclei if the initial kinetic energy of each nucleus is greater than that calculated in (ii)....[1] [2] 9702/41/M/J/10 [Turn over

10 10 5 (a) A constant current is maintained in a long straight vertical wire. A Hall probe is positioned a distance r from the centre of the wire, as shown in Fig current-carrying wire Hall probe X Y r terminals to Hall probe circuitry and voltmeter Fig. 5.1 (i) Explain why, when the Hall probe is rotated about the horizontal axis XY, the Hall voltage varies between a maximum positive value and a maximum negative value....[2] (ii) The maximum Hall voltage V H is measured at different distances r. Data for V H and the corresponding values of r are shown in Fig V H / V r / cm Fig. 5.2 It is thought that V H and r are related by an expression of the form where k is a constant. V H = k r 9702/41/M/J/10

11 11 1. Without drawing a graph, use data from Fig. 5.2 to suggest whether the expression is valid. [2] 2. A graph showing the variation with 1 r of V H is plotted. State the features of the graph that suggest that the expression is valid [1] (b) The Hall probe in (a) is now replaced with a small coil of wire connected to a sensitive voltmeter. The coil is arranged so that its plane is normal to the magnetic field of the wire. (i) State Faraday s law of electromagnetic induction and hence explain why the voltmeter indicates a zero reading....[3] (ii) State three different ways in which an e.m.f. may be induced in the coil [3] 9702/41/M/J/10 [Turn over

12 12 6 A student is asked to design a circuit by which a direct voltage of peak value 9.0 V is obtained from a 240 V alternating supply. The student uses a transformer that may be considered to be ideal and a bridge rectifier incorporating four ideal diodes. The partially completed circuit diagram is shown in Fig V + load Fig. 6.1 (a) On Fig. 6.1, draw symbols for the four diodes so as to produce the polarity across the load as shown on the diagram. [2] (b) Calculate the ratio number of turns on the secondary coil number of turns on the primary coil. ratio =... [3] 9702/41/M/J/10

13 13 7 Negatively-charged particles are moving through a vacuum in a parallel beam. The particles have speed v. The particles enter a region of uniform magnetic field of flux density 930 μt. Initially, the particles are travelling at right-angles to the magnetic field. The path of a single particle is shown in Fig negatively-charged particles, speed v arc of radius 7.9 cm uniform magnetic field, flux density 930 μt Fig. 7.1 The negatively-charged particles follow a curved path of radius 7.9 cm in the magnetic field. A uniform electric field is then applied in the same region as the magnetic field. an electric field strength of 12 kv m 1, the particles are undeviated as they pass through the region of the fields. (a) On Fig. 7.1, mark with an arrow the direction of the electric field. [1] (b) Calculate, for the negatively-charged particles, (i) the speed v, v =... m s 1 [3] (ii) the ratio charge mass. 9702/41/M/J/10 ratio =... C kg 1 [3] [Turn over

14 14 8 A π 0 meson is a sub-atomic particle. A stationary π 0 meson, which has mass kg, decays to form two γ-ray photons. The nuclear equation for this decay is π 0 γ + γ. (a) Explain why the two γ-ray photons have the same energy [2] (b) Determine, for each γ-ray photon, (i) the energy, in joule, energy =... J [2] (ii) the wavelength, wavelength =... m [2] 9702/41/M/J/10

15 15 (iii) the momentum. momentum =... N s [2] 9702/41/M/J/10 [Turn over

16 16 Section B Answer all the questions in the spaces provided. 9 The circuit diagram of Fig. 9.1 is an amplifier circuit incorporating an operational amplifier (op-amp). 4.2 kω 1.0 kω +9 V 1.5 V + 9 V V + Fig. 9.1 (a) (i) On Fig. 9.1, mark, with the letter X, the virtual earth. [1] (ii) Explain what is meant by a virtual earth....[3] (b) In bright sunlight, the light-dependent resistor (LDR) has resistance 200 Ω. (i) Calculate, for the LDR in bright sunlight, the voltmeter reading. reading =... V [3] 9702/41/M/J/10

17 (ii) 17 The sunlight incident on the LDR becomes less bright. State and explain the effect on the voltmeter reading of this decrease in brightness....[3] 9702/41/M/J/10 [Turn over

18 18 10 (a) Briefly explain the principles of CT scanning [6] 9702/41/M/J/10

19 19 (b) A simple section through a body consists of four voxels, as illustrated in Fig section directions of viewing Fig An X-ray image of the section is obtained by viewing along each of the directions shown in Fig The detector readings for each direction of viewing are summed to give the pattern of readings shown in Fig Fig any one direction, the total of the detector readings is 16. (i) the pattern of readings of Fig. 10.2, state the magnitude of the background reading. background reading =... [1] (ii) On Fig. 10.1, mark the pattern of pixels for the four-voxel section. [2] 9702/41/M/J/10 [Turn over

20 20 11 Many radio stations now broadcast on FM rather than on AM. In general, FM is broadcast at much higher frequencies than AM. (a) Explain what is meant by FM (frequency modulation) [2] (b) State two advantages and two disadvantages of FM transmissions when compared with AM transmissions. advantages of FM transmissions disadvantages of FM transmissions [4] 9702/41/M/J/10

21 21 12 A ground station on Earth transmits a signal of frequency 14 GHz and power 18 kw towards a communications satellite orbiting the Earth, as illustrated in Fig ground station, signal power 18 kw signal frequency 14 GHz satellite Earth Fig The loss in signal power between the ground station and the satellite is 190 db. (a) Calculate the power of the signal received by the satellite. power =... W [3] (b) The signal received by the satellite is amplified and transmitted back to Earth. (i) Suggest a frequency for the signal that is sent back to Earth. frequency =... GHz [1] (ii) Give a reason for your answer in (i)....[1] 9702/41/M/J/10 [Turn over

22 22 BLANK PAGE 9702/41/M/J/10

23 23 BLANK PAGE 9702/41/M/J/10

24 24 BLANK PAGE Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. 9702/41/M/J/10

25 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level * * PHYSICS 9702/42 Paper 4 A2 Structured Questions May/June 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. Answer all questions. You may lose marks if you do not show your working or if you do not use appropriate units. 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 question Total This document consists of 20 printed pages. DC (LEO/DJ) 17381/5 [Turn over

26 2 Data speed of light in free space, c = ms 1 permeability of free space, μ 0 = 4π 10 7 Hm 1 permittivity of free space, ε 0 = Fm 1 elementary charge, the Planck constant, unified atomic mass constant, rest mass of electron, rest mass of proton, e = C h = Js u = kg m e = kg m p = kg molar gas constant, R = 8.31 J K 1 mol 1 the Avogadro constant, N A = mol 1 the Boltzmann constant, k = JK 1 gravitational constant, G = Nm 2 kg 2 acceleration of free fall, g = 9.81 m s /42/M/J/10

27 3 mulae uniformly accelerated motion, s = ut at 2 v 2 = u 2 + 2as work done on/by a gas, W = pδv gravitational potential, hydrostatic pressure, φ = Gm r p = ρgh pressure of an ideal gas, p = 1 3 Nm V <c 2 > simple harmonic motion, velocity of particle in s.h.m., a = ω 2 x v = v 0 cos ωt v = ± ω (x 2 0 x 2 ) electric potential, V = Q 4πε 0 r capacitors in series, 1/C = 1/C 1 + 1/C capacitors in parallel, C = C 1 + C energy of charged capacitor, W = 1 2 QV resistors in series, R = R 1 + R resistors in parallel, 1/R = 1/R 1 + 1/R alternating current/voltage, radioactive decay, x = x 0 sin ωt x = x 0 exp( λt) decay constant, λ = t /42/M/J/10 [Turn over

28 4 Section A Answer all the questions in the spaces provided. 1 (a) Define gravitational potential at a point [2] (b) The Earth may be considered to be an isolated sphere of radius R with its mass concentrated at its centre. The variation of the gravitational potential φ with distance x from the centre of the Earth is shown in Fig distance x 0 0 R 2R 3R 4R 5R 2.0 / 10 7 J kg Fig. 1.1 The radius R of the Earth is m. (i) By considering the gravitational potential at the Earth s surface, determine a value for the mass of the Earth. 9702/42/M/J/10 mass =... kg [3]

29 (ii) 5 A meteorite is at rest at infinity. The meteorite travels from infinity towards the Earth. Calculate the speed of the meteorite when it is at a distance of 2R above the Earth s surface. Explain your working. (iii) speed =... m s 1 [4] In practice, the Earth is not an isolated sphere because it is orbited by the Moon, as illustrated in Fig initial path of meteorite Moon Earth Fig. 1.2 (not to scale) The initial path of the meteorite is also shown. Suggest two changes to the motion of the meteorite caused by the Moon [2] 9702/42/M/J/10 [Turn over

30 6 2 A long strip of springy steel is clamped at one end so that the strip is vertical. A mass of 65 g is attached to the free end of the strip, as shown in Fig springy steel mass 65 g clamp displacement / cm Fig. 2.1 The mass is pulled to one side and then released. The variation with time t of the horizontal displacement of the mass is shown in Fig t / s 1 2 Fig. 2.2 The mass undergoes damped simple harmonic motion. (a) (i) Explain what is meant by damping.... [2] 9702/42/M/J/10

31 (ii) (b) (i) 7 Suggest, with a reason, whether the damping is light, critical or heavy.... [2] Fig. 2.2 to determine the frequency of vibration of the mass. frequency =... Hz [1] (ii) Hence show that the initial energy stored in the steel strip before the mass is released is approximately 3.2 mj. [2] (c) After eight complete oscillations of the mass, the amplitude of vibration is reduced from 1.5 cm to 1.1 cm. State and explain whether, after a further eight complete oscillations, the amplitude will be 0.7 cm [2] 9702/42/M/J/10 [Turn over

32 8 3 (a) The resistance of a thermistor at 0 C is 3840 Ω. At 100 C the resistance is 190 Ω. When the thermistor is placed in water at a particular constant temperature, its resistance is 2300 Ω. (i) Assuming that the resistance of the thermistor varies linearly with temperature, calculate the temperature of the water. temperature =... C [2] (ii) The temperature of the water, as measured on the thermodynamic scale of temperature, is 286 K. By reference to what is meant by the thermodynamic scale of temperature, comment on your answer in (i).... [3] (b) A polystyrene cup contains a mass of 95 g of water at 28 C. A cube of ice of mass 12 g is put into the water. Initially, the ice is at 0 C. The water, of specific heat capacity J kg 1 K 1, is stirred until all the ice melts. Assuming that the cup has negligible mass and that there is no heat exchange with the atmosphere, calculate the final temperature of the water. The specific latent heat of fusion of ice is J kg 1. temperature =... C [4] 9702/42/M/J/10

33 9 4 Two point charges A and B each have a charge of C. They are separated in a vacuum by a distance of 12.0 μm, as shown in Fig μm A P Q B C C 3.0 μm 3.0 μm Fig. 4.1 Points P and Q are situated on the line AB. Point P is 3.0 μm from charge A and point Q is 3.0 μm from charge B. (a) Calculate the force of repulsion between the charges A and B. force =... N [3] (b) Explain why, without any calculation, when a small test charge is moved from point P to point Q, the net work done is zero [2] (c) Calculate the work done by an electron in moving from the midpoint of line AB to point P. work done =... J [4] 9702/42/M/J/10 [Turn over

34 10 5 (a) State two functions of capacitors in electrical circuits [2] (b) Three capacitors, each marked 30 μf, 6 V max, are arranged as shown in Fig A B Fig. 5.1 Determine, for the arrangement shown in Fig. 5.1, (i) the total capacitance, capacitance =... μf [2] (ii) the maximum potential difference that can safely be applied between points A and B. potential difference =... V [2] 9702/42/M/J/10

35 11 (c) A capacitor of capacitance 4700 μf is charged to a potential difference of 18 V. It is then partially discharged through a resistor. The potential difference is reduced to 12 V. Calculate the energy dissipated in the resistor during the discharge. energy =... J [3] 9702/42/M/J/10 [Turn over

36 12 6 (a) A uniform magnetic field has constant flux density B. A straight wire of fixed length carries a current I at an angle θ to the magnetic field, as shown in Fig magnetic field flux density B I current-carrying wire Fig. 6.1 (i) The current I in the wire is changed, keeping the angle θ constant. On Fig. 6.2, sketch a graph to show the variation with current I of the force F on the wire. F 0 0 I Fig. 6.2 [2] 9702/42/M/J/10

37 (ii) 13 The angle θ between the wire and the magnetic field is now varied. The current I is kept constant. On Fig. 6.3, sketch a graph to show the variation with angle θ of the force F on the wire. F / Fig. 6.3 [3] (b) A uniform magnetic field is directed at right-angles to the rectangular surface PQRS of a slice of a conducting material, as shown in Fig uniform magnetic field Q R P S direction of movement of electrons Fig. 6.4 Electrons, moving towards the side SR, enter the slice of conducting material. The electrons enter the slice at right-angles to side SR. (i) Explain why, initially, the electrons do not travel in straight lines across the slice from side SR to side PQ.... [2] (ii) Explain to which side, PS or QR, the electrons tend to move.... [2] 9702/42/M/J/10 [Turn over

38 14 7 (a) Explain what is meant by the root-mean-square (r.m.s.) value of an alternating voltage [2] (b) An alternating voltage V is represented by the equation V = 220 sin(120πt), where V is measured in volts and t is in seconds. this alternating voltage, determine (i) the peak voltage, peak voltage =... V [1] (ii) the r.m.s. voltage, r.m.s. voltage =... V [1] (iii) the frequency. frequency =... Hz [1] (c) The alternating voltage in (b) is applied across a resistor such that the mean power output from the resistor is 1.5 kw. Calculate the resistance of the resistor. resistance =... Ω [2] 9702/42/M/J/10

39 15 8 Americium-241 is an artificially produced radioactive element that emits α-particles. A sample of americium-241 of mass 5.1 μg is found to have an activity of Bq. (a) Determine, for this sample of americium-241, (i) the number of nuclei, number =... [2] (ii) the decay constant, decay constant =... s 1 [2] (iii) the half-life, in years. half-life =... years [2] (b) Another radioactive element has a half-life of approximately 4 hours. Suggest why measurement of the mass and activity of a sample of this element is not appropriate for the determination of its half-life [1] 9702/42/M/J/10 [Turn over

40 16 Section B Answer all the questions in the spaces provided. 9 (a) Negative feedback may be used in amplifier circuits. State (i) what is meant by negative feedback,... [2] (ii) two effects of negative feedback on an amplifier incorporating an operational amplifier (op-amp) [2] (b) Fig. 9.1 is a circuit for an amplifier that is used with a microphone. P microphone 120 kω V OUT R Fig. 9.1 The output potential difference V OUT is 4.4 V when the potential at point P is 62 mv. Determine (i) the gain of the amplifier, 9702/42/M/J/10 gain =... [1]

41 17 (ii) the resistance of the resistor R. resistance =... Ω [2] (c) The maximum potential produced by the microphone at point P on Fig. 9.1 is 95 mv. The power supply for the operational amplifier may be either +/ 5 V or +/ 9 V. State which power supply should be used. Justify your answer quantitatively [3] 9702/42/M/J/10 [Turn over

42 18 10 (a) State the name of an electrical sensing device that will respond to changes in (i) length,... [1] (ii) pressure.... [1] (b) A relay is sometimes used as the output of a sensing circuit. The output of a particular sensing circuit is either + 2 V or 2 V. On Fig. 10.1, draw symbols for a relay and any other necessary component so that the external circuit is switched on only when the output from the sensing circuit is + 2 V. +2 V or 2 V output from sensing circuit terminals of external circuit Fig [4] 9702/42/M/J/10

43 19 11 Explain the main principles behind the generation of ultrasound to obtain diagnostic information about internal body structures [6] 9702/42/M/J/10 [Turn over

44 20 12 A telephone link between two towns is to be provided using an optic fibre. The length of the optic fibre between the two towns is 75 km. (a) State two changes that occur in a signal as it is transmitted along an optic fibre [2] (b) The optic fibre has an attenuation per unit length of 1.6 db km 1. The minimum permissible signal-to-noise power ratio in the fibre is 25 db. The average noise power in the optic fibre is W. (i) Suggest one reason why power ratios are expressed in db.... [1] (ii) The signal input power to the optic fibre is designed to be 6.5 mw. Determine whether repeater amplifiers are necessary in the optic fibre between the two towns. [5] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. 9702/42/M/J/10

45 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level * * PHYSICS 9702/43 Paper 4 A2 Structured Questions May/June 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. Answer all questions. You may lose marks if you do not show your working or if you do not use appropriate units. 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 question Total This document consists of 20 printed pages. DC (SM/DJ) [Turn over

46 2 Data speed of light in free space, c = ms 1 permeability of free space, μ 0 = 4π 10 7 Hm 1 permittivity of free space, ε 0 = Fm 1 elementary charge, the Planck constant, unified atomic mass constant, rest mass of electron, rest mass of proton, e = C h = Js u = kg m e = kg m p = kg molar gas constant, R = 8.31 J K 1 mol 1 the Avogadro constant, N A = mol 1 the Boltzmann constant, k = JK 1 gravitational constant, G = Nm 2 kg 2 acceleration of free fall, g = 9.81 m s /43/M/J/10

47 3 mulae uniformly accelerated motion, s = ut at 2 v 2 = u 2 + 2as work done on/by a gas, W = pδv gravitational potential, hydrostatic pressure, φ = Gm r p = ρgh pressure of an ideal gas, p = 1 3 Nm V <c 2 > simple harmonic motion, velocity of particle in s.h.m., a = ω 2 x v = v 0 cos ωt v = ± ω (x 2 0 x 2 ) electric potential, V = Q 4πε 0 r capacitors in series, 1/C = 1/C 1 + 1/C capacitors in parallel, C = C 1 + C energy of charged capacitor, W = 1 2 QV resistors in series, R = R 1 + R resistors in parallel, 1/R = 1/R 1 + 1/R alternating current/voltage, radioactive decay, x = x 0 sin ωt x = x 0 exp( λt) decay constant, λ = t /43/M/J/10 [Turn over

48 4 Section A Answer all the questions in the spaces provided. 1 (a) Define gravitational potential at a point [2] (b) The Earth may be considered to be an isolated sphere of radius R with its mass concentrated at its centre. The variation of the gravitational potential φ with distance x from the centre of the Earth is shown in Fig distance x 0 0 R 2R 3R 4R 5R 2.0 / 10 7 J kg Fig. 1.1 The radius R of the Earth is m. (i) By considering the gravitational potential at the Earth s surface, determine a value for the mass of the Earth. 9702/43/M/J/10 mass =... kg [3]

49 (ii) 5 A meteorite is at rest at infinity. The meteorite travels from infinity towards the Earth. Calculate the speed of the meteorite when it is at a distance of 2R above the Earth s surface. Explain your working. (iii) speed =... m s 1 [4] In practice, the Earth is not an isolated sphere because it is orbited by the Moon, as illustrated in Fig initial path of meteorite Moon Earth Fig. 1.2 (not to scale) The initial path of the meteorite is also shown. Suggest two changes to the motion of the meteorite caused by the Moon [2] 9702/43/M/J/10 [Turn over

50 6 2 A long strip of springy steel is clamped at one end so that the strip is vertical. A mass of 65 g is attached to the free end of the strip, as shown in Fig springy steel mass 65 g clamp displacement / cm Fig. 2.1 The mass is pulled to one side and then released. The variation with time t of the horizontal displacement of the mass is shown in Fig t / s 1 2 Fig. 2.2 The mass undergoes damped simple harmonic motion. (a) (i) Explain what is meant by damping.... [2] 9702/43/M/J/10

51 (ii) (b) (i) 7 Suggest, with a reason, whether the damping is light, critical or heavy.... [2] Fig. 2.2 to determine the frequency of vibration of the mass. frequency =... Hz [1] (ii) Hence show that the initial energy stored in the steel strip before the mass is released is approximately 3.2 mj. [2] (c) After eight complete oscillations of the mass, the amplitude of vibration is reduced from 1.5 cm to 1.1 cm. State and explain whether, after a further eight complete oscillations, the amplitude will be 0.7 cm [2] 9702/43/M/J/10 [Turn over

52 8 3 (a) The resistance of a thermistor at 0 C is 3840 Ω. At 100 C the resistance is 190 Ω. When the thermistor is placed in water at a particular constant temperature, its resistance is 2300 Ω. (i) Assuming that the resistance of the thermistor varies linearly with temperature, calculate the temperature of the water. temperature =... C [2] (ii) The temperature of the water, as measured on the thermodynamic scale of temperature, is 286 K. By reference to what is meant by the thermodynamic scale of temperature, comment on your answer in (i).... [3] (b) A polystyrene cup contains a mass of 95 g of water at 28 C. A cube of ice of mass 12 g is put into the water. Initially, the ice is at 0 C. The water, of specific heat capacity J kg 1 K 1, is stirred until all the ice melts. Assuming that the cup has negligible mass and that there is no heat exchange with the atmosphere, calculate the final temperature of the water. The specific latent heat of fusion of ice is J kg 1. temperature =... C [4] 9702/43/M/J/10

53 9 4 Two point charges A and B each have a charge of C. They are separated in a vacuum by a distance of 12.0 μm, as shown in Fig μm A P Q B C C 3.0 μm 3.0 μm Fig. 4.1 Points P and Q are situated on the line AB. Point P is 3.0 μm from charge A and point Q is 3.0 μm from charge B. (a) Calculate the force of repulsion between the charges A and B. force =... N [3] (b) Explain why, without any calculation, when a small test charge is moved from point P to point Q, the net work done is zero [2] (c) Calculate the work done by an electron in moving from the midpoint of line AB to point P. work done =... J [4] 9702/43/M/J/10 [Turn over

54 10 5 (a) State two functions of capacitors in electrical circuits [2] (b) Three capacitors, each marked 30 μf, 6 V max, are arranged as shown in Fig A B Fig. 5.1 Determine, for the arrangement shown in Fig. 5.1, (i) the total capacitance, capacitance =... μf [2] (ii) the maximum potential difference that can safely be applied between points A and B. potential difference =... V [2] 9702/43/M/J/10

55 11 (c) A capacitor of capacitance 4700 μf is charged to a potential difference of 18 V. It is then partially discharged through a resistor. The potential difference is reduced to 12 V. Calculate the energy dissipated in the resistor during the discharge. energy =... J [3] 9702/43/M/J/10 [Turn over

56 12 6 (a) A uniform magnetic field has constant flux density B. A straight wire of fixed length carries a current I at an angle θ to the magnetic field, as shown in Fig magnetic field flux density B I current-carrying wire Fig. 6.1 (i) The current I in the wire is changed, keeping the angle θ constant. On Fig. 6.2, sketch a graph to show the variation with current I of the force F on the wire. F 0 0 I Fig. 6.2 [2] 9702/43/M/J/10

57 (ii) 13 The angle θ between the wire and the magnetic field is now varied. The current I is kept constant. On Fig. 6.3, sketch a graph to show the variation with angle θ of the force F on the wire. F / Fig. 6.3 [3] (b) A uniform magnetic field is directed at right-angles to the rectangular surface PQRS of a slice of a conducting material, as shown in Fig uniform magnetic field Q R P S direction of movement of electrons Fig. 6.4 Electrons, moving towards the side SR, enter the slice of conducting material. The electrons enter the slice at right-angles to side SR. (i) Explain why, initially, the electrons do not travel in straight lines across the slice from side SR to side PQ.... [2] (ii) Explain to which side, PS or QR, the electrons tend to move.... [2] 9702/43/M/J/10 [Turn over

58 14 7 (a) Explain what is meant by the root-mean-square (r.m.s.) value of an alternating voltage [2] (b) An alternating voltage V is represented by the equation V = 220 sin(120πt), where V is measured in volts and t is in seconds. this alternating voltage, determine (i) the peak voltage, peak voltage =... V [1] (ii) the r.m.s. voltage, r.m.s. voltage =... V [1] (iii) the frequency. frequency =... Hz [1] (c) The alternating voltage in (b) is applied across a resistor such that the mean power output from the resistor is 1.5 kw. Calculate the resistance of the resistor. resistance =... Ω [2] 9702/43/M/J/10

59 15 8 Americium-241 is an artificially produced radioactive element that emits α-particles. A sample of americium-241 of mass 5.1 μg is found to have an activity of Bq. (a) Determine, for this sample of americium-241, (i) the number of nuclei, number =... [2] (ii) the decay constant, decay constant =... s 1 [2] (iii) the half-life, in years. half-life =... years [2] (b) Another radioactive element has a half-life of approximately 4 hours. Suggest why measurement of the mass and activity of a sample of this element is not appropriate for the determination of its half-life [1] 9702/43/M/J/10 [Turn over

60 16 Section B Answer all the questions in the spaces provided. 9 (a) Negative feedback may be used in amplifier circuits. State (i) what is meant by negative feedback,... [2] (ii) two effects of negative feedback on an amplifier incorporating an operational amplifier (op-amp) [2] (b) Fig. 9.1 is a circuit for an amplifier that is used with a microphone. P microphone 120 kω V OUT R Fig. 9.1 The output potential difference V OUT is 4.4 V when the potential at point P is 62 mv. Determine (i) the gain of the amplifier, 9702/43/M/J/10 gain =... [1]

61 17 (ii) the resistance of the resistor R. resistance =... Ω [2] (c) The maximum potential produced by the microphone at point P on Fig. 9.1 is 95 mv. The power supply for the operational amplifier may be either +/ 5 V or +/ 9 V. State which power supply should be used. Justify your answer quantitatively [3] 9702/43/M/J/10 [Turn over

62 18 10 (a) State the name of an electrical sensing device that will respond to changes in (i) length,... [1] (ii) pressure.... [1] (b) A relay is sometimes used as the output of a sensing circuit. The output of a particular sensing circuit is either + 2 V or 2 V. On Fig. 10.1, draw symbols for a relay and any other necessary component so that the external circuit is switched on only when the output from the sensing circuit is + 2 V. +2 V or 2 V output from sensing circuit terminals of external circuit Fig [4] 9702/43/M/J/10

63 19 11 Explain the main principles behind the generation of ultrasound to obtain diagnostic information about internal body structures [6] 9702/43/M/J/10 [Turn over

64 20 12 A telephone link between two towns is to be provided using an optic fibre. The length of the optic fibre between the two towns is 75 km. (a) State two changes that occur in a signal as it is transmitted along an optic fibre [2] (b) The optic fibre has an attenuation per unit length of 1.6 db km 1. The minimum permissible signal-to-noise power ratio in the fibre is 25 db. The average noise power in the optic fibre is W. (i) Suggest one reason why power ratios are expressed in db.... [1] (ii) The signal input power to the optic fibre is designed to be 6.5 mw. Determine whether repeater amplifiers are necessary in the optic fibre between the two towns. [5] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. 9702/43/M/J/10

65 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level * * PHYSICS 9702/41 Paper 4 A2 Structured Questions October/November 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. Answer all questions. You may lose marks if you do not show your working or if you do not use appropriate units. 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 question Total This document consists of 24 printed pages. DC (LEO/SW) 23673/4 [Turn over

66 2 Data speed of light in free space, c = ms 1 permeability of free space, μ 0 = 4π 10 7 Hm 1 permittivity of free space, ε 0 = Fm 1 elementary charge, the Planck constant, unified atomic mass constant, rest mass of electron, rest mass of proton, e = C h = Js u = kg m e = kg m p = kg molar gas constant, R = 8.31 J K 1 mol 1 the Avogadro constant, N A = mol 1 the Boltzmann constant, k = JK 1 gravitational constant, G = Nm 2 kg 2 acceleration of free fall, g = 9.81 m s /41/O/N/10

67 3 mulae uniformly accelerated motion, s = ut at 2 v 2 = u 2 + 2as work done on/by a gas, gravitational potential, hydrostatic pressure, W = pδv φ = Gm r p = ρgh pressure of an ideal gas, p = 1 3 simple harmonic motion, velocity of particle in s.h.m., electric potential, V = a = ω 2 x Nm V <c 2 > v = v 0 cos ωt v = ± ω (x 2 0 x 2 ) Q 4πε 0 r capacitors in series, 1/C = 1/C 1 + 1/C capacitors in parallel, C = C 1 + C energy of charged capacitor, W = 1 2 QV resistors in series, R = R 1 + R resistors in parallel, 1/R = 1/R 1 + 1/R alternating current/voltage, x = x 0 sin ωt radioactive decay, x = x 0 exp( λt) decay constant, λ = t /41/O/N/10 [Turn over

68 4 Section A Answer all the questions in the spaces provided. 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 g s. 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. 1.0g s gravitational field strength 0.8g s 0.6g s 0.4g s 0.2g s 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 kg and kg respectively. The radius of the Earth is R E and the separation of the centres of the Earth and the Moon is 60 R E, as illustrated in Fig R E Earth mass 6.00 x kg Moon mass 7.40 x kg 60 R E Fig. 1.2 (not to scale) 9702/41/O/N/10

69 (i) (ii) 5 Explain why there is a point between the Earth and the Moon at which the gravitational field strength is zero....[2] Determine the distance, in terms of R E, from the centre of the Earth at which the gravitational field strength is zero. (iii) distance =...R E [3] 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 of Earth surface of Moon distance Fig. 1.3 [3] 9702/41/O/N/10 [Turn over

70 6 2 (a) (i) State the basic assumption of the kinetic theory of gases that leads to the conclusion that the potential energy between the atoms of an ideal gas is zero....[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 P volume / 10 4 m Q R pressure / 10 5 Pa Fig /41/O/N/10

71 (i) 7 State the change in internal energy of the gas during one complete cycle PQRP. change =... J [1] (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 change work done on gas / J heating supplied to gas / J increase in internal energy / J P Q Q R R P Fig. 2.2 Complete Fig. 2.2 to show all of the energy changes. [3] 9702/41/O/N/10 [Turn over

72 8 3 A student sets up the apparatus illustrated in Fig. 3.1 in order to investigate the oscillations of a metal cube suspended on a spring. pulley variable-frequency oscillator spring thread 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 amplitude / mm frequency / Hz Fig. 3.2 (a) (i) State the phenomenon illustrated in Fig [1] (ii) the maximum amplitude of vibration, state the magnitudes of the amplitude and the frequency. amplitude =... mm frequency =... Hz [1] 9702/41/O/N/10

73 9 (b) The oscillations of the metal cube of mass 150 g may be assumed to be simple harmonic. your answers in (a)(ii) to determine, for the metal cube, (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] 9702/41/O/N/10 [Turn over

74 10 4 (a) Define capacitance [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. 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] 9702/41/O/N/10

75 (ii) 11 the charge, in coulomb, on the sphere. 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] 9702/41/O/N/10 [Turn over

76 12 5 Positive ions are travelling through a vacuum in a narrow beam. The ions enter a region of uniform magnetic field of flux density B and are deflected in a semi-circular arc, as shown in Fig detector uniform magnetic field 12.8 cm beam of positive ions Fig. 5.1 The ions, travelling with speed 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 C. Show that the magnetic flux density is T. Explain your working. [3] 9702/41/O/N/10

77 13 (c) Ions of mass 22 u with the same charge and speed as those in (b) are also present in the beam. (i) On Fig. 5.1, sketch the path of these ions in the magnetic field of magnetic flux density 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] 9702/41/O/N/10 [Turn over

78 14 6 A simple iron-cored transformer is illustrated in Fig iron core input output primary coil secondary 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] 9702/41/O/N/10

79 15 (b) The root-mean-square (r.m.s.) voltage and current in the primary coil are V P and I P respectively. The r.m.s. voltage and current in the secondary coil are V S and I S respectively. (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, V S V P = I P I S. [2] 9702/41/O/N/10 [Turn over

80 16 7 (a) State an effect, one in each case, that provides evidence for (i) the wave nature of a particle,...[1] (ii) the particulate nature of electromagnetic radiation....[1] (b) Four electron energy levels in an atom are shown in Fig J electron energy J J J Fig. 7.1 (not to scale) An emission spectrum is associated with the electron transitions between these energy levels. this spectrum, (i) state the number of lines,...[1] (ii) calculate the minimum wavelength. wavelength =... m [2] 9702/41/O/N/10

81 17 8 In some power stations, nuclear fission is used as a source of energy. (a) State what is meant by nuclear fission [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 B Li +... [3] (c) Suggest why, when neutrons are absorbed in the boron rods, the rods become hot as a result of this nuclear reaction [3] 9702/41/O/N/10 [Turn over

82 18 Section B Answer all the questions in the spaces provided. 9 An amplifier circuit incorporating an operational amplifier (op-amp) is shown in Fig R 2 +9 V + 9 V V IN R 1 V OUT Fig. 9.1 (a) State (i) the name of this type of amplifier circuit,...[1] (ii) the gain G in terms of resistances R 1 and R 2....[1] 9702/41/O/N/10

83 19 (b) The value of R 1 is 820 Ω. The resistor of resistance R 2 is replaced with a light-dependent resistor (LDR). The input potential difference V IN is 15 mv. Calculate the output potential difference V OUT for the LDR having a resistance of (i) 100 Ω (the LDR is in sunlight), V OUT =... V [2] (ii) 1.0 MΩ (the LDR is in darkness). V OUT =... V [1] 9702/41/O/N/10 [Turn over

84 20 10 (a) (i) State what is meant by the acoustic impedance of a medium....[1] (ii) Data for some media are given in Fig medium air gel soft tissue bone speed of ultrasound acoustic impedance / m s 1 / kg m 2 s Fig data from Fig 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 boundary incident intensity I reflected intensity I R acoustic impedance Z 1 transmitted intensity I T acoustic impedance Z 2 Fig The media have acoustic impedances of Z 1 and Z 2. The transmitted intensity of the ultrasound beam is I T and the reflected intensity is I R. (i) State the relation between I, I T and I R....[1] 9702/41/O/N/10

85 (ii) 21 The reflection coefficient a is given by the expression a = (Z 2 Z 1 )2 (Z 2 + Z 1 ) 2. data from Fig to determine the reflection coefficient a for a boundary between 1. gel and soft tissue, 2. air and soft tissue. a =...[2] 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] 9702/41/O/N/10 [Turn over

86 22 11 (a) Wire pairs provide one means of communication but they are subject to high levels of noise and attenuation. Explain what is meant by (i) noise,...[1] (ii) attenuation....[1] (b) A microphone is connected to a receiver using a wire pair, as shown in Fig wire pair microphone receiver Fig The wire pair has an attenuation per unit length of 12 db km 1. The noise power in the wire pair is W. The microphone produces a signal power of 2.9 lw. (i) Calculate the maximum length of the wire pair so that the minimum signal-to-noise ratio is 24 db. length =... m [4] (ii) Communication over distances greater than that calculated in (i) is required. Suggest how the circuit of Fig may be modified so that the minimum signal-to-noise ratio at the receiver is not reduced....[2] 9702/41/O/N/10