Cambridge A Level Physics 9702 — 2021 May/June Paper 3 · Variant 4

1 In this experiment, you will investigate the oscillations of a chain. (a) (i) ● Assemble the apparatus as shown in Fig. 1.1 with each nail held securely in a boss and at the same height above the bench. Position the stands so that the distance between the nails is approximately 60 cm. ≈ 60 cm boss boss nail nail stand stand chain of paper clips benchbench Fig. 1.1 ● Rest one of the metre rules on the nails, as shown in Fig. 1.2. C nail nail metre rule Fig. 1.2 ● The vertical distance between the horizontal metre rule and the lowest part of the chain is C. Using the other metre rule, measure and record C. C = ................................................... cm [1] (ii) ● Push the bottom of the chain a short distance away from you. Release it so that it swings towards and away from you. ● Take measurements to determine the period T of these oscillations. T = ......................................................... [2] (b) Repeat (a) with different distances between the stands until you have six sets of values of C and T. All values of C must be greater than 15 cm. 1 1 Record your results in a table. Include values of and in your table. T C [9] 1 1(c) (i) Plot a graph of on the y-axis against on the x-axis. [3] T C (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 T and C are related by the equation 1 a = + b T C 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] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a)(i) Value of C to the nearest mm. 1 1(a)(ii) Value of T with unit and in the range 0.50–1.50 s. 1 At least two measurements of nT where n ⩾ 5. 1 1(b) Six sets of readings of C and T (different values) with correct trend (T increases as C increases) and without help from the Supervisor scores 4 marks, five sets scores 3 marks etc. 4 Range: Cmin ⩽ 18.0 cm and Cmax ⩾ 35.0 cm. 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 / √C / cm–½, 1 / T (s–1). 1 Consistency: All values of raw times must be given to the nearest 0.1 s or all to the nearest 0.01 s. 1 Significant figures: Values of 1 / √C must be given to the same number of significant figures as, or one greater than, the number of significant figures in C. 1 Calculation: Values of 1 / √C calculated correctly. 1 Question Answer Marks 1(c)(i) Axes: Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Axes must be labelled with the quantity that is being plotted. Scale markings should be no more than three large squares apart. 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 x and y directions. 1 Quality: All points in the table must be plotted (at least 5) on the grid. Trend of points must be correct. It must be possible to draw a straight line that is within ± 5.0 × 10–3 cm–½ (± 5.0 × 10–2 m–½) on the 1 / √C axis (normally x- axis) of all plotted points. 1 1(c)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate’s line (at least 5 points). There must be an even distribution of points either side of the line along the full length. Allow one anomalous point only if clearly indicated by the candidate. There must be at least five points left after the anomalous point is disregarded. Lines must not be kinked or thicker than half a small square. 1 1(c)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct, i.e. Δy / Δx. Gradient sign on answer line matches graph drawn. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: Correct read-off from a point on the line and substituted into y = mx + c. Read-off must be accurate to half a small square in both x and y directions. or Intercept read directly from the graph at x = 0, accurate to half a small square. 1 Question Answer Marks 1(d) Value of a equal to candidate’s gradient and value of b equal to candidate’s intercept. Values must not be written as fractions. 1 Units for a and b correct, e.g. cm½ s–1 for a and s–1 for b. 1

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2 In this experiment, you will investigate the deformation of a foam ring. (a) (i) ● Assemble the apparatus as shown in Fig. 2.1. The wooden rod should pivot freely on the nail. stand nail boss wooden rod clamp bench ≈ 6 cm Fig. 2.1 ● Take the larger of the two foam rings. ● Using the metre rule, measure and record the inner diameter D1 and the outer diameter D2 , as shown in Fig. 2.2. D1 D2 foam ring Fig. 2.2 D1 = ........................................................ mm D2 = ........................................................ mm [2] (ii) Estimate the percentage uncertainty in your value of D2. Show your working. percentage uncertainty = ......................................................... [1] (b) ● Position the ring under the line on the rod and centrally on the wooden block, as shown in Fig. 2.3. line h1 wooden block Fig. 2.3 ● Adjust the height of the boss so that the rod is horizontal. ● The vertical distance, next to the ring, of the top of the rod above the block is h1, as shown in Fig. 2.3. Using the calipers, measure and record h1. h1 = ........................................................ mm ● Place the slotted mass at the end of the rod, as shown in Fig. 2.4. slotted mass h2 Fig. 2.4 ● The vertical distance, next to the ring, of the top of the rod above the block is now h2, as shown in Fig. 2.4. Measure and record h2. h2 = ........................................................ mm ● Calculate y where y = h1 – h2. y = ........................................................ mm [2] (c) (i) The distance between the nail and the line is A and the distance between the nail and the centre of the slotted mass is B, as shown in Fig. 2.5. B slotted A mass Fig. 2.5 Measure and record A and B. A = ......................................................... cm B = ......................................................... cm [1] (ii) Calculate the additional force F on the ring using mgB F = A where g = 9.81 N kg–1 and m = 0.100 kg. F = ..................................................... N [1] (iii) Justify the number of significant figures you have given for your value of F. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1]

Mark scheme: 2(a)(i) Values of D1 and D2 both to nearest mm. 1 Evidence of repeat readings for D1 and D2. 1 2(a)(ii) Percentage uncertainty based on an absolute uncertainty of 2–5 mm. If repeat readings have been taken, then the absolute uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(b) All values of h1 and h2 to nearest 0.1 mm or all to nearest 0.01 mm. 1 Correct calculation of y. 1 2(c)(i) Values of A and B recorded and A < B. 1 2(c)(ii) Correct calculation of F. 1 2(c)(iii) Justification for significant figures in F linked to s.f. in B and A. 1 2(d) Second values of D1, D2, h1 and h2. 1 y smaller for smaller D2. 1 2(e)(i) Two values of k calculated correctly. 1 2(e)(ii) Valid comment relating to the calculated values of k, testing against a criterion specified by the candidate. 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 Difficult to judge/determine whether rod is horizontal. C Difficult to measure h with reason e.g. parallax error/wooden block or ring getting in way. D Large percentage uncertainty in y. E Difficult to measure A or B with reason e.g. judging centre of slotted mass when measuring B/judging centre of nail for A or B/parallax error in A or B/difficult to hold ruler steady when measuring A or B. (Allow parallax error linked to h or A or B only once.) 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 Improved method to determine if rod horizontal e.g. use a spirit level/use set square(s) with description of method. C Method to reduce error in measuring h e.g. use wider rod/move ring to edge of block/use travelling microscope. D Method to reduce percentage uncertainty in y e.g. measure change in height at end of rod/use larger mass/increase B. E Improved method of measuring A or B e.g. clamp ruler/method to locate and mark centre of slotted mass e.g. measure diameter and halve to find radius. 1 mark for each point up to a maximum of 4. 4

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