Cambridge A Level Physics 9702 — 2025 Oct/Nov Paper 5 · Variant 2

1 Fig. 1.1 shows a model wind turbine with blades, each of length L, placed in moving air. L moving air blade terminals turbine bench Fig. 1.1 The area of the circle swept by the blades of the turbine is A. The output of the turbine has two terminals. The turbine is connected to a resistor of resistance R. At a speed v of the moving air, the current in the resistor is I. The atmospheric pressure is P and the thermodynamic temperature of the air is T. It is suggested that I is related to v by the relationship I2R APv3 = Q 2T where Q is a constant. Plan a laboratory experiment to test the relationship between I and v. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine a value for Q. In your plan you should include: • 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: Question Answer Marks 1 Defining the problem vary v and measure I or v is the independent variable and I is the dependent variable 1 keep A and R constant 1 Methods of data collection labelled diagram of workable experiment including: 1 • fan positioned in line with the turbine so that blades of both fan and turbine overlap • fan on bench • fan labelled and one other label from bench, turbine, blade(s) (of turbine), terminals, L workable circuit diagram showing resistor connected to an ammeter in series with the terminals of the turbine using correct 1 circuit symbols method to vary v, e.g. change speed of fan / change distance between fan and blades / vary current in or p.d. across fan 1 method to determine temperature T, e.g. use a thermometer 1 Method of Analysis plot a graph of I2 against v3 or equivalent (e.g. lg I against lg v or 2 ln I against ln v) 1 relationship valid if a straight line is produced passing through the origin 1 (For lg I against lg v: relationship valid if a straight line with gradient = 1.5 is produced) 2TR  gradient 1 Q = AP 2TR  10 2 y -intercept (For lg I against lg v: Q = ) AP 1 Additional detail including safety considerations 6 D1 precaution with reason linked to (moving) fan blades / turbine blades, e.g. keep away from the fan to avoid (moving) blades or use a screen around the fan / turbine to avoid (moving) blades or precaution with reason linked to prevent air / dust particles in eye, e.g. use goggles to avoid air stream (into eye) D2 clamp turbine / fan to bench D3 keep P and T constant D4 T = t + 273 D5 method to determine A: use a rule(r) / calipers to measure L and A = L2 D6 repeat measurements of L in different positions / different blades and average D7 method to measure v, e.g. use an anemometer or air speed meter or method to measure P, e.g. use a manometer or barometer or pressure gauge D8 wait for steady / constant air flow / movement of blades / current D9 method to determine R, e.g.: separate circuit showing ohmmeter connected to R only or terminals of turbine connected correctly to resistor and ammeter and voltmeter across resistor and R = V / I or separate workable circuit with power supply resistor, ammeter and voltmeter across R and R = V / I D10 method to check temperature / pressure is constant, e.g. measure temperature / pressure several times / before and after

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2 A student observes the orbits of some of the moons around the planet Saturn, as shown in Fig. 2.1. Tethys Rhea Mimas Saturn Pandora Enceladus Dione Fig. 2.1 (not to scale) For the moon Pandora, the period of the orbit and the mean distance from the centre of Saturn are determined. The measurements of period T and mean distance r are repeated for other moons. It is suggested that T and r are related by the equation 2πr n T = k where n and k are constants. (a) A graph is plotted of lg T on the y‑axis against lg r on the x‑axis. Determine expressions for the gradient and y‑intercept. gradient = ............................................................... y‑intercept = ............................................................... [1] (b) Values of r and T are given for different moons in Table 2.1. Table 2.1 moon r / 108 m T / 103 s lg (r / 108 m) lg (T / 103 s) Pandora 1.42 52 ± 5 Mimas 1.86 81 ± 5 Enceladus 2.38 120 ± 10 Tethys 2.95 170 ± 10 Dione 3.77 240 ± 20 Rhea 5.28 390 ± 30 Calculate and record values of lg (r / 108 m) and lg (T / 103 s) in Table 2.1. Include the absolute uncertainties in lg (T / 103 s). [2] (c) (i) Plot a graph of lg (T / 103 s) against lg (r / 108 m). Include error bars for lg (T / 103 s). [2] (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines. [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 = n 1 2  y-intercept = lg k 2(b) 1 lg (r / 108 m) lg (T / 103 s) 0.152 or 0.1523 (1.72 or 1.716)  0.04 0.270 or 0.2695 (1.91 or 1.908)  0.03 0.377 or 0.3766 (2.08 or 2.079 or 2.0792)  0.04 0.470 or 0.4698 (2.23 or 2.230 or 2.2304)  0.03 0.576 or 0.5763 (2.38 or 2.380 or 2.3802)  0.04 0.723 or 0.7226 (2.59 or 2.591 or 2.5911)  0.03 Values of lg (r / 108 m) and lg (T / 103 s) correct as shown above. Uncertainties in lg (T / 103 s) correct as shown above. 1 2(c)(i) Six points from (b) plotted correctly. 1 Must be within half a small square. Diameter of points must be less than half a small square. Error bars in lg (T / 103 s) plotted correctly. 1 All error bars must be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 2(c)(ii) Straight line of best fit drawn. 1 Thickness of the line must be less than half a small square. Do not accept line from top point to bottom point. Line must pass between (0.19, 1.80) and (0.21, 1.80) and between (0.645, 2.50) and (0.66, 2.50). Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). 1 Thickness of the line must be less than half a small square. All error bars must be plotted. 2(c)(iii) Gradient determined with clear substitution of data points into y / x. 1 Distance between data points must be greater than half the length of the drawn line. Gradient determined of worst acceptable line with clear substitution of data points into y / x. 1 uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 2(c)(iv) y-intercept determined by substitution of correct point with consistent powers of ten into y = mx + c. 1 y-intercept of worst acceptable line determined by substitution 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) Do not accept ECF from false origin method. 2(d) Value of n determined using gradient and n and k given to 2 or 3 significant figures. 1 n = gradient = (c)(iii) Value of k determined using y-intercept. 1 Correct method must be seen. 2 2 k = = 10 y -intercept 10(c)(iv) Absolute uncertainties in n and k determined. 1 Absolute uncertainty in n = absolute uncertainty in gradient and 2 2 =k − 10 y -intercept 10 WAL y -intercept Correct method must be seen. 2(e) r determined to a minimum of 2 significant figures from (c)(iii) and (c)(iv) or (d) with correct substitution and correct power 1 of ten. lg1380 − y -intercept r = 10 gradient  10 8 or k  1380 r = n  10 8 2π

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