Cambridge A Level Physics 9702 — 2017 May/June Paper 5 · Variant 2

1 A student is investigating the motion of a small cube on a turntable connected to an electric motor as shown in Fig. 1.1. turntable cube r Fig. 1.1 The cube is placed at a distance r from the centre of the turntable. It is suggested that the relationship between r and the maximum frequency f of the turntable for which the cube does not move relative to the turntable is K = 4π2mfr where m is the mass of the cube and K is a constant. Design a laboratory experiment to test the relationship between f and r. Explain how your results could be used to determine a value for K. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to • the procedure to be followed, • the measurements to be taken, • the control of variables, • the analysis of the data, • any safety precautions to be taken. 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Mark scheme: 1 Defining the problem r is the independent variable and f (frequency of turntable) is the dependent variable or vary r and measure f (frequency of turntable) 1 keep m constant 1 Methods of data collection labelled diagram showing power supply connected to motor (two leads) within turntable; circuits must be workable 1 method to change frequency of rotation of the turntable, e.g. adjust output of (variable) power supply or adjust variable resistor 1 increase frequency until the cube moves (relative to the turntable) 1 method to determine period of rotation of the turntable, e.g. stopwatch, light gate attached to a timer/data-logger or stroboscope 1 Method of analysis plots a graph of f against 1 / r (allow log f against log r) 1 relationship valid if a straight line produced passing through the origin (for lg f vs. lg r straight line of gradient of –1) 1 K = gradient × 4π2m (for lg f vs. lg r, K = 10y-intercept × 4π2m) 1 Question Answer Marks Additional detail including safety considerations Max. 6 D1 use safety screen D2 time at least 10 rotations of turntable or detailed use of stroboscope D3 f = 1 / T for correct determination of period of rotation of turntable D4 repeat experiment for each r and average f D5 use balance to measure mass of cube D6 wait for turntable to rotate steadily before increasing frequency or gradual/incremental/slowly increase in frequency D7 use a spirit level to check that turntable is horizontal or clean cube/surface D8 use a rule to measure r D9 method to ensure r is measured to the centre of the cube, e.g. put a mark on the cube or align front or back of cube by a set distance D10 method to determine centre of the turntable e.g. measure two or more diameters/maximum distance ideas

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2 A student is investigating the current in a circuit. The circuit is set up as shown in Fig. 2.1. E A I P Q Fig. 2.1 Two resistors P and Q are connected to a power supply of e.m.f. E and negligible internal resistance. The current I is measured. The resistance of resistor P is P. The experiment is repeated for different values of P. It is suggested that I and P are related by the equation E = I(P + Q) where Q is the resistance of resistor Q. 1 (a) A graph is plotted of on the y-axis against P on the x-axis. I Determine expressions for the gradient and the y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of P and I are given in Fig. 2.2. The tolerance of each value of P is ±5%. 1 P / Ω I / mA / A–1 I 180 ± 34 220 ± 28 330 ± 19 470 ± 14 560 ± 12 680 ± 10 Fig. 2.2 1 Calculate and record values of / A–1 in Fig. 2.2. I Determine the absolute uncertainties in P. [2] 1(c) (i) Plot a graph of / A–1 against P / Ω. I Include error bars for P. [2] (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = ...........................................................[2]

Mark scheme: 2(a) gradient = 1 E y-intercept = Q E 1 2(b) P / Ω 1 I / A–1 ± 9 29 or 29.4 ± 11 36 or 35.7 ± 16.5 53 or 52.6 ± 23.5 71 or 71.4 ± 28 83 or 83.3 ± 34 100 First mark for uncertainties correct. Allow 1 s.f. e.g. 10, 10, 20, 20, 30, 30. Second mark for all second column correct. Allow a mixture of significant figures. 2 2(c)(i) Six points plotted correctly. Must be accurate to less than half a small square. No “blobs”. Diameter of points must be less than half a small square. 1 Error bars in P plotted correctly. All error bars to be plotted. Length of bar must be accurate to less than half a small square and symmetrical. 1 Question Answer Marks 2(c)(ii) Line of best fit drawn. If points are plotted correctly then lower end of line should pass between (200, 32) and (200, 34) and upper end of line should pass between (600, 88) and (600, 91). 1 Worst acceptable line drawn (steepest or shallowest possible line). All error bars must be plotted. 1 2(c)(iii) Gradient determined with a triangle that is at least half the length of the drawn line. 1 uncertainty = gradient of line of best fit – gradient of worst acceptable line or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 1 2(c)(iv) y-intercept determined by substitution of correct point into y = mx + c. 1 uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line or uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept) 1 Question Answer Marks 2(d)(i) E determined using gradient and units for E and Q with correct power of ten. = = 1 1 gradient 2(c)(iii) E 1 Q determined using y-intercept and E and Q given to 2 or 3 significant figures. Correct substitution of numbers must be seen. = × = × = = -intercept 2(c)(iv) -intercept 2(c)(iv) gradient 2(c)(iii) y Q E y E 1 2(d)(ii) % uncertainty in E = % uncertainty in gradient 1 % uncertainty in Q = % uncertainty in E + % uncertainty in y-intercept or % uncertainty in Q = % uncertainty in gradient + % uncertainty in y-intercept. Correct substitution of numbers must be seen. Maximum/minimum methods: = × max -intercept Max max -intercept max or mingradient y Q y E = × min -intercept Min min -intercept min or max gradient y Q y E 1

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