# A-level PHYSICS A PHYA4/2. Unit 4 Fields and Further Mechanics. Section B. Monday 20 June 2016 Morning

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1 Please write clearly in block capitals. Centre number Candidate number Surname Forename(s) Candidate signature A-level PHYSICS A Unit 4 Fields and Further Mechanics Section B Monday 20 June 2016 Morning Materials For this paper you must have: a calculator a ruler a Data and Formulae Booklet (enclosed). Time allowed: The total time for both sections of this paper is 1 hour 45 minutes. You are advised to spend approximately one hour on this section. Instructions Use black ink or black ball-point pen. Fill in the es at the top of this page. Answer all questions. You must answer the questions in the space provided. Answers written in margins or on blank pages will not be marked. Do all rough work in this book. Cross through any work you do not want to be marked. Show all your working. Information The marks for questions are shown in brackets. The maximum mark for this paper is 50. You are expected to use a calculator where appropriate. A Data and Formulae Booklet is provided as a loose insert. You will be marked on your ability to: use good English organise information clearly use specialist vocabulary where appropriate. (JUN16PHYA4201) WMP/Jun16/E3 PHYA4/2

2 2 Section B Answer all questions. You are advised to spend approximately one hour on this section. 1 (a) Figure 1 shows how the charge Q stored by a capacitor varies with the potential difference (pd) V across it as V is increased from 9.0 V to 12.0 V. Figure Q / μc pd / V 1 (a) (i) Use Figure 1 to determine an accurate value for the capacitance of the capacitor. [2 marks] capacitance = μf 1 (a) (ii) Calculate the additional energy stored by the capacitor when V is increased from 9.0 V to 12.0 V. [3 marks] additional energy = J (02)

3 3 1 (b) When a 470 μf capacitor is discharged through a fixed resistor R, the pd across it decreases by 80% in 45 s. 1 (b) (i) Calculate the time constant of the capacitor resistor circuit. [3 marks] time constant = s 1 (b) (ii) Determine the resistance of R. [2 marks] resistance = Ω 1 (b) (iii) At which point during the discharging process is the capacitor losing charge at the smallest rate? Tick ( ) the correct answer. [1 mark] if correct when the charge on the capacitor is greatest when energy is dissipated at the greatest rate when the current in the resistor is greatest when the pd across R is least 11 Turn over (03)

4 4 2 The planet Venus may be considered to be a sphere of uniform density kg m 3. The gravitational field strength at the surface of Venus is 8.87 N kg 1. 2 (a) (i) Show that the gravitational field strength g s at the surface of a planet is related to the the density ρ and the radius R of the planet by the expression where G is the gravitational constant. g 4 s = πgrρ 3 [2 marks] 2 (a) (ii) Calculate the radius of Venus. Give your answer to an appropriate number of significant figures. [3 marks] radius = m (04)

5 5 2 (b) At a certain time, the positions of Earth and Venus are aligned so that the distance between them is a minimum. Sketch a graph on the axes below to show how the magnitude of the gravitational field strength g varies with distance along the shortest straight line between their surfaces. Consider only the contributions to the field produced by Earth and Venus. Mark values on the vertical axis of your graph. [3 marks] gravitational field strength / N kg 1 0 surface of Earth distance surface of Venus 8 Turn over for the next question Turn over (05)

6 6 3 (a) State the condition for momentum to be conserved in a system. [1 mark] 3 (b) When a stationary unstable nucleus emits an α particle with velocity v the resulting nucleus recoils with velocity V, as shown in Figure 2. Figure 2 recoiling nucleus α particle V N m v The mass of the α particle is m and the mass of the recoiling nucleus is N. 3 (b) (i) Show how the principle of conservation of momentum may be used to derive an expression for V in terms of N, m and v. [2 marks] (06)

7 7 3 (b) (ii) Assume that all of the energy released in the emission process is transferred as kinetic energy to the α particle and the recoiling nucleus. The total energy released is E. Use your result from part (b)(i) to show that the kinetic energy of the α particle is given by ( ) E α = N N + m E [4 marks] 3 (c) (i) The isotope of radon Rn decays by emitting an α particle. State the nucleon number of the recoiling nucleus. [1 mark] nucleon number = Question 3 continues on the next page Turn over (07)

8 8 3 (c) (ii) The total energy released when a nucleus of Rn decays is J. Calculate the magnitude of the momentum of the α particle. State an appropriate unit for your answer. Mass of a nucleon = kg [4 marks] momentum = unit 3 (d) Explain why the expressions in parts (b)(i) and (b)(ii) could not be applied when an unstable nucleus decays by emitting a β particle. [1 mark] 13 (08)

9 9 Turn over for the next question DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Turn over (09)

10 10 4 Within certain limits, the bob of a simple pendulum of length l may be considered to move with simple harmonic motion of period T, where T = 2π l g 4 (a) State one limitation that applies to the pendulum when this equation is used. [1 mark] 4 (b) Describe an experiment to determine the value of the Earth s gravitational field strength g using a simple pendulum and any other appropriate apparatus. In your answer you should: describe how you would arrange the apparatus indicate how you would make the measurements explain how you would calculate the value of g by a graphical method state the experimental procedures you would use to ensure that your result was accurate. You may draw a diagram to help you with your answer. The quality of your written communication will be assessed in your answer. [6 marks] (10)

11 11 Question 4 continues on the next page Turn over (11)

12 12 4 (c) When carrying out the experiment in part (b), a student measures the time period incorrectly. Mistakenly, the student thinks that the time period is the time taken for half of an oscillation instead of a full oscillation, as illustrated in Figure 3. Figure 3 full oscillation half oscillation Deduce the effect this will have on the value of g obtained from the experiment, explaining how you arrive at your answer. [3 marks] 10 (12)

13 13 Turn over for the next question DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Turn over (13)

14 14 5 (a) State, in words, the two laws of electromagnetic induction. [3 marks] Law 1 Law 2 5 (b) Figure 4 illustrates the main components of one type of electromagnetic braking system. A metal disc is attached to the rotating axle of a vehicle. An electromagnet is mounted with its pole pieces placed either side of the rotating disc, but not touching it. When the brakes are applied, a direct current is passed through the coil of the electromagnet and the disc slows down. Figure 4 coil electromagnet pole piece axle metal disc Turn over (14)

15 15 5 (b) (i) Explain, using the laws of electromagnetic induction, how the device in Figure 4 acts as an electromagnetic brake. [3 marks] 5 (b) (ii) A conventional braking system has friction pads that are brought into contact with a moving metal surface when the vehicle is to be slowed down. State one advantage and one disadvantage of an electromagnetic brake compared to a conventional brake. [2 marks] Advantage Disadvantage 8 END OF QUESTIONS (15)

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