Cambridge A Level Physics 9702 — 2025 May/June Paper 3 · Variant 1

1 In this experiment, you will investigate the oscillation of masses on springs. You have been provided with masses and springs. Set up the apparatus as shown in Fig. 1.1. wooden rod boss stand double spring spring 100 g mass hanger mass S and 100 g mass bench Fig. 1.1 (a) ● Ensure the bottoms of both masses are at the same level. ● Pull both masses down through a short distance and release them at the same time. ● Watch the oscillations of the masses. The masses initially oscillate in phase, then out of phase and then back in phase. ● The number of oscillations of mass S from release until the masses are back in phase for the first time is n0. Determine and record n0. n0 = ......................................................... [2] (b) (i) ● Add a mass of 30 g to mass S. The added mass is M. ● Record M. M = ............................................................... ● Repeat (a). The number of oscillations of mass S from release until the masses are back in phase for the first time is n. ● Determine and record n. n = ............................................................... [1] (ii) Calculate N, where N = n0 – n. N = ......................................................... [1] (c) Vary M by changing the number of 10 g masses added to mass S and determine n. Do not use M = 0. Repeat until you have five sets of values of M and n. Record your results in a table. Include values of N. Also include values of N 3 to three significant figures. [8] (d) (i) Plot a graph of N 3 on the y-axis against M on the x-axis. [3] (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (e) It is suggested that the quantities N and M are related by the equation N 3 = PM + Q where P and Q are constants. Using your answers in (d)(iii), determine the values of P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] [Total: 20]

Mark scheme: Question Answer Marks 1(a) Final value of n0 with no unit and in the range 10 ⩽ n0 ⩽ 30. 1 Evidence of repeats. 1 1(b)(i) n ˂ n0. 1 1(b)(ii) Correct calculation of N. 1 1(c) Five sets of readings of M (different values) and n with correct trend (M increases, n decreases) and without help from 4 Supervisor scores 4 marks, four sets scores 3 marks, etc. Range of M: Must include Mmin = 10 g and Mmax ⩾ 60 g. 1 Column headings: 1 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. M / g. Significant figures: All values of N 3 given to 3 significant figures. 1 Calculation: Correct calculation of N 3. 1 1(d)(i) Axes: 1 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, no awkward scales (e.g. 3:10 or fractions). Plotting of points: 1 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 x and y directions. Quality: 1 All N3 values are positive and trend of points must be positive. All points in the table (at least 4 points) must be plotted on the grid for this mark to be awarded. It must be possible to draw a straight line that is within  5 g on the M-axis of all plotted points. 1(d)(ii) Line of best fit: 1 ‘Best fit’ is judged by the balance of all points on the grid (at least 4 points) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Lines must not be kinked or thicker than half a square. Some candidates may choose to identify an anomalous point. If 5 or more points are plotted and 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. 1(d)(iii) Gradient: 1 The hypotenuse of the triangle used must 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. Method of calculation must be correct, not x / y. Gradient sign on answer line must be consistent with graph drawn. y-intercept: 1 Intercept read directly from the graph, with read-off at M = 0, accurate to half a small square in y direction. or Correct read-off from a point on the line is substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. 1(e) Value of P = candidate’s gradient value and value of Q = candidate’s intercept value. 1 Values must not be written as fractions or given to only one significant figure. Units for P: g–1 or kg–1 consistent with their readings 1 and no units for Q.

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2 In this experiment, you will investigate the behaviour of paper on water. You have been provided with two sheets of tracing paper. (a) ● On one of the sheets of tracing paper, draw two identical rectangles as shown in Fig. 2.1 where c = 4.0 cm and d = 6.0 cm. The orientation of the rectangles must be as shown in Fig. 2.1. ● Add labels A and B to the rectangles, as shown in Fig. 2.1. short side of tracing paper B c long side of A d tracing paper d c Fig. 2.1 ● Use the scissors to cut out the rectangles. ● Take measurements to determine the average value of d. d = ................................................... cm [1] (b) (i) ● When A is placed flat on the surface of the water in one of the bowls, the shape will curl up as shown in Fig. 2.2. Two edges of the paper will curl and then meet. edge edge Fig. 2.2 The time between placing A on the water and the two edges meeting is TA. ● Place A flat on the water. ● Determine TA. TA = ............................................................... ● Remove A from the water and place it in the empty bowl. [2] (ii) Estimate the percentage uncertainty in your value of TA. Show your working. percentage uncertainty = ...................................................... % [1] (c) (i) ● Repeat the procedure in (b)(i) for B. The time between placing B on the water and the two edges meeting is TB. TB = ............................................................... ● Remove B from the water. ● Compare your values of TA and TB. Record the longer time. longer time = ............................................................... [1] (ii) The quantity W is given by longer time W = . shorter time Calculate W. W = ......................................................... [1] (iii) Justify the number of significant figures that you have given for your value of W. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (d) Repeat (a), (b)(i), (c)(i) and (c)(ii) using new rectangles with c = 4.0 cm and d = 9.0 cm. d = ......................................................... cm TA = ............................................................... TB = ............................................................... longer time = ............................................................... W = ............................................................... [3]

Mark scheme: 2(a) At least two values of raw d all to the nearest mm 1 and final d in the range 5.9–6.1 cm. 2(b)(i) Value of TA on answer line in the range 2.0−10.0 s with unit. 1 Repeats: At least two measurements of TA. 1 2(b)(ii) Percentage uncertainty based on absolute uncertainty in TA in range 0.5–3.0 s. 1 Correct method of calculation to find percentage uncertainty e.g. (absolute uncertainty / value from (b)(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. 2(c)(i) Value of TB. 1 2(c)(ii) Correct calculation of W with no unit and W > 1. 1 2(c)(iii) Justification for significant figures in W linked to significant figures in TA and TB (only). 1 2(d) Second value of d. 1 Second values of TA and TB. 1 Second value of W > first value of W. 1 2(e) Two values of k calculated correctly. 1 The final k values must not be written as fractions or given to only one significant figure. 2(f) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 20%, leading to a consistent conclusion. 2(g)(i) A Two (sets of) readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few 4 readings”). B Reason for difficulty in producing the rectangle of paper e.g. hard to make the sides parallel (or perpendicular) / hard to cut the sides straight / difficult to cut lengths accurately / cutting by hand with scissors (produces wavy sides) / paper twists / folds when cutting (because it is thin). C Difficulty with measuring T with reason e.g. two edges are not parallel when they meet / difficult to ensure the stopwatch is started at the same time as the paper is placed (or dropped) on to the water / experiment cannot be repeated using the same piece of paper. D Difficulty with the paper staying central in the bowl e.g. paper floats / moves and touches the edge of bowl. E Reason for difficulty with placing the paper onto the water surface e.g. paper is tilted / is dropped / hard to lower the paper parallel to the water / water surface is disturbed / ripples when placing paper / paper gets wet before entering water / paper is curled before placing on water. 1 mark for each point up to a maximum of 4. 2(g)(ii) A Take more readings (for different values of d) and plot a graph or take more readings and compare k values (not 4 “repeat readings” on its own). B (To produce the rectangles) use a template / a grid or place tracing paper on graph paper or use a set square to draw (the rectangle) or use a guillotine / paper or box cutter / knife / scalpel with a straight edge (or ruler). C Video / film / record with timer in view. D Use wider bowl or have the water surface further down from the top of the bowl. E Place paper on a flat sheet of metal / glass / filter paper and place that sheet on surface of water or valid method of flattening the paper before putting into the water e.g. place weight on paper. 1 mark for each point up to a maximum of 4.

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