10   13 A ‘tennis trainer’ consists of a tennis ball suspended by a string from the top of a vertical pole. When the ball is hit it travels in a horizontal circle around the pole, as shown in both the photograph and the diagram. string tennis ball 1.2 m vertical pole The radius of the path of the ball is 1.2 m and the speed of the ball is 3.8 m s−1. Deduce whether these values are consistent with the angle between the string and the vertical pole shown in the photograph. ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... (Total for Question 13 = 5 marks) Turn over 11   BLANK PAGE 12   14 Power supplies provide either alternating or direct currents and potential differences. (a) A power supply produces an alternating potential difference (p.d.). The p.d. has a period of 0.02 s and a peak value of 4.0 V. (i) Calculate the frequency of the supply. (1) ................................................................................................................................................................................................................................................... Frequency = ....................................................... (ii) Calculate the root‑mean‑square p.d. (1) ................................................................................................................................................................................................................................................... Root‑mean‑square p.d. = ....................................................... (b) It is possible to convert alternating currents and p.d.s, to direct currents and p.d.s using diodes. The power supply provides an input Vin to the circuit shown. The circuit includes four diodes D1, D2, D3 and D4 and a resistor R. The circuit produces an output potential difference Vout . D1 D4 D3 D2 R Y X Vin Vout A graph of Vin against time and a corresponding graph of Vout against time are shown below. Vin Vout Time Time Turn over 13   (i) Explain the operation of this circuit. Your answer should refer to D1, D2, D3 and D4. (3) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... (ii) A capacitor is added between points X and Y in the circuit. The new graph of Vout against time is shown below. Vout / V 4 3 2 1 0 30 20 10 0 Time / ms Determine a value for the capacitance of the capacitor. resistance of R = 2.2 kΩ (3) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... Capacitance = ....................................................... (Total for Question 14 = 8 marks) 14   15 A series of experiments was carried out in the 1970s to investigate the structure of protons using the linac at Stanford, USA. *(a) Explain how an electron is accelerated in a linac. (6) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... (b) The electron leaves the accelerator with a high energy. Explain why electrons need high energies to investigate the structure of a proton. (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... Turn over 15   (c) An electron leaves the accelerator with a momentum of 20 GeV / c. (i) Explain, with reference to base units, why GeV / c can be used as a unit of momentum. (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... (ii) An electron with initial momentum 20 GeV / c collides with a stationary proton. After the collision the electron is deflected by an angle of 20° as shown and its momentum is 9.1 GeV / c. The momentum of the proton after the collision is 11.9 GeV / c. 20° initial direction of electron proton Deduce whether the law of conservation of momentum is obeyed. (3) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... (iii) The collisions between electrons and the protons in these experiments are sometimes inelastic. State what is meant by an inelastic collision. (1) ................................................................................................................................................................................................................................................... (Total for Question 15 = 14 marks) 16   16 A device called a clutch can be used to connect a motor to a load. The diagram shows a design called an eddy current clutch. motor magnet copper disc plastic disc Side view motor magnet copper disc plastic disc load Several magnets are embedded in the plastic disc and it is rotated by the motor. (a) (i) Explain why a current is induced in the copper disc when the motor is switched on. (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... (ii) Explain, using Lenz’s law, why the copper disc rotates. 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Turn over 17   (b) The motor rotates at 500 revolutions per minute. Calculate the angular speed ω of the motor. (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ω = ....................................................... (c) The table shows how the turning effect exerted on a load varies with ω for a particular distance between the copper disc and the plastic disc. ω / rad s−1 Turning effect / N cm 52.4 1.0 104.7 2.0 157.1 2.8 Explain the trend shown by the data. (4) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... (Total for Question 16 = 11 marks)