Cambridge A Level Physics 9702 — 2024 May/June Paper 3 · Variant 4

1 In this experiment, you will investigate the equilibrium position of a pulley system. (a) ● Assemble the apparatus as shown in Fig. 1.1 with the rods of the stands approximately 50 cm apart. nail held in boss boss pulley string central pulley plumb line θ Q stand M stand G-clamp G-clamp ≈ 50 cm bench Fig. 1.1 ● Adjust the pulley fixed to the stand so that the top of the pulley is approximately 60 cm above the bench. ● Adjust the boss holding the nail so that the nail is approximately 60 cm above the bench. ● Use some of the slotted masses to add a mass of 70 g to Q. ● The mass added to Q is x. Record the value of x. x = ............................................................ g ● The angle between the plumb line and the string is θ, as shown in Fig. 1.1. Measure and record θ. θ = ............................................................ ° ● Carefully remove the slotted masses from Q. [1] (b) By using different numbers of slotted masses, vary x. For each value of x, measure θ. Repeat until you have six sets of values of x and θ. 1 Record your results in a table. Include values of in your table. cos θ [10] 1 (c) (i) Plot a graph of on the y-axis against x on the x-axis. [3] cos θ (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (d) It is suggested that the quantities θ and x are related by the equation 1 = ax + b cos θ where a and b are constants. Use your answers in (c)(iii) to determine the values of a and b. Give appropriate units. a = ............................................................... b = ............................................................... [2] (e) The mass of M is M and the mass of Q is Q. The constants a and b are related to M and Q by 2 2Q a = and b = . M M Calculate values for M and Q. M = ............................................................ g Q = ............................................................ g [1] [Total: 20]

Mark scheme: 1(a) 1 1(b) Six sets of readings of x (different values) and  with correct trend (as x increases, average  increases) and without help from the Supervisor scores 5 marks, five sets scores 4 marks, etc. 5 Range: xmin ⩽ 20 g and xmax ⩾ 200 g. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit must conform to accepted scientific convention e.g.  /°. 1 / cos  must have no unit. 1 Consistency: All values of  must be given to the nearest degree. 1 Significant figures: Values of 1 / cos  given to same number of s.f. as (or one more than) the number of s.f. in . 1 Calculation: Values of 1 / cos  calculated correctly 1 1(c)(i) Axes: Axes must be labelled with the required quantities. Scales must be chosen so that the plotted points occupy at least half the graph grid in both the x and y directions. Scale markings are no more than 2 cm (one large square) apart. Sensible scales must be used. Scales must not be awkward (e.g. 3:10 or fractions). 1 Plotting of points: All observations in the table must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square. Points must be plotted to an accuracy of half a small square in both the x and y directions. 1 Quality: All points in the table (at least 5) must be plotted on the grid. Trend must be correct. It must be possible to draw a straight line that is within  0.20 on the 1 / cos  axis of all plotted points. 1 Question Answer Marks 1(c)(ii) Line of best fit: ‘Best fit’ is judged by balance of all points on the grid (at least 5 points) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Line must not be kinked or thicker than half a small square. Some candidates may choose to identify an anomalous point. If they identify one point as anomalous (e.g. by circling or labelling) then this point is to be disregarded when judging the line of best fit. There must be at least 5 points left after the anomalous point is disregarded. 1 1(c)(iii) Gradient: The hypotenuse of the triangle used should be greater than half the length of the drawn line. Both read-offs must be accurate to half a small square in both the x and y directions. The method of calculation must be correct, not x / y. The gradient sign on the answer line must be consistent with the graph drawn. 1 y-intercept: Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both the x and y directions. or Intercept read directly from the graph, with read-off at x = 0 accurate to half a small square in y direction. 1 1(d) Value of a = candidate’s gradient and value of b = candidate’s intercept. The values must not be written as fractions or given to only one significant figure. 1 Unit for a correct and consistent with x readings (e.g. g–1) and no unit for b. 1 1(e) Correct calculation of Q. 1

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2 In this experiment, you will investigate the effect of air resistance on a spinning card. (a) (i) ● Assemble the apparatus as shown in Fig. 2.1, with the washer and plastic tube over the nail. plastic tube slot nail (inside tube) washer bench pulley wooden block G-clamp string mass P Fig. 2.1 ● Rotate the plastic tube so that P rises until it just touches the pulley. ● Release the plastic tube so that P falls. ● Measure and record the time T0 for P to reach the end of its fall. T0 = ......................................................... [2] (ii) Estimate the percentage uncertainty in your value of T0. Show your working. percentage uncertainty = ..................................................... % [1] (b) (i) Fig. 2.2 shows card A. L A W Fig. 2.2 Measure and record the length L and the width W of the card, as shown in Fig. 2.2. L = ............................................................... W = ............................................................... [1] (ii) ● Insert the card centrally into the slot at the top of the plastic tube with its length horizontal. If necessary, use a small piece of adhesive putty to fix it securely in the slot. ● Rotate the plastic tube so that P rises until it just touches the pulley. ● Release the plastic tube and measure the time T for P to reach the end of its fall. T = ......................................................... [2] (c) Repeat (b) using the card marked B. L = ............................................................... W = ............................................................... T = ............................................................... [3] (d) It is suggested that the relationship between T, T0, L and W is k(T – T0) = L2W where k is a constant. (i) Using your data, calculate two values of k. first value of k = ............................................................... second value of k = ............................................................... [1] (ii) Justify the number of significant figures that you have given for your values of k. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1]

Mark scheme: 2(a)(i) Value for T0 in range 0.20–2.00s with unit. 1 Evidence of repeat measurements of T0. 1 2(a)(ii) Absolute uncertainty in T0 in range 0.2–0.5 s. Correct method of calculation to find percentage uncertainty e.g. (absolute uncertainty/value from (a)(i))  100. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. 1 2(b)(i) Values for L and W to the nearest mm with unit and L > W. 1 2(b)(ii) All raw value(s) for T to the nearest 0.1s or all raw value(s) to nearest 0.01 s with unit. 1 Value of T > T0. 1 2(c) Second values of L and W. 1 Second value of T. 1 Value of second T greater than first T. 1 2(d)(i) Two values of k calculated correctly. The final k values must not be written as fractions or given to only one significant figure. 1 2(d)(ii) Justification based on the significant figures in (T – T0), W and L. 1 2(e) Calculation of percentage difference between candidate’s two k values. Comparison of percentage difference with 15% leading to a consistent conclusion. 1 Question Answer Marks 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B T0 is short so large uncertainty / large percentage uncertainty in T0. C Difficult to judge/determine/decide whether P has just touched the pulley or difficulty maintaining the same release point. D Difficult to judge/determine/decide when mass just reaches the end of its fall. E Difficulties with card with reason e.g. judging if central in slot / ensuring card is horizontal. 1 mark for each point up to a maximum of 4. 4 2(f)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Increase the fall distance. C Use pointer at the starting point / use a stop. D Record/film/video with timer or record/film/video and view frame-by-frame or use a position/distance sensor placed below or above mass and a data logger. E Measure to find position of centre of the card and mark it or use spirit level (to check the card is horizontal) or other workable method to check card is horizontal. 1 mark for each point up to a maximum of 4. 4

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