Cambridge A Level Physics 9702 — 2022 Oct/Nov Paper 3 · Variant 1

1 In this experiment, you will investigate oscillations of card shapes. (a) You have been provided with a circular card of radius 10.0 cm. ● Draw a circle on the card of radius 9.0 cm, as shown in Fig. 1.1. card 9.0 cm Fig. 1.1 (not to scale) ● Fold the card in half. Cut carefully along the line, as shown in Fig. 1.2, and keep both parts of the card. folded edge folded edge Fig. 1.2 (not to scale) ● The distance between the centre of one side of the card shape and the centre of the other side is d, as shown in Fig. 1.3. d folded edge folded edge card shape Fig. 1.3 Measure and record d. d = ......................................................... [1] (b) ● Stand the card shape on the bench. ● Adjust the loops of card until the distance between the points where the loops touch the bench is approximately 3 cm, as shown in Fig. 1.4. loops of card bench ≈ 3 cm Fig. 1.4 ● Gently press down one side of the card shape through a short distance. Release the card shape so that it oscillates. ● Determine the period T of these oscillations. T = ......................................................... [2] (c) Use the remaining card to cut out shapes of smaller radius, each with the same width of 1.0 cm. For each card shape, measure d and repeat (b). Repeat until you have five sets of values of d and T. Record your results in a table. Include values of T 2 in your table. [8] (d) (i) Plot a graph of T 2 on the y‑axis against d 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 T and d are related by the equation T 2 = Ad + B where A and B are constants. Using your answers in (d)(iii), determine the values of A and B. Give appropriate units. A = ............................................................... B = ............................................................... [2] (f) Theory suggests that 2π2 A = g where g is the acceleration of free fall. Use your value of A in (e) to determine a value for g. Give an appropriate unit. g = ......................................................... [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: Question Answer Marks 1(a) Value of d with unit and in the range 18.0–20.0 cm. 1 1(b) Value of T on the answer line with unit and in the range 0.4–1.0 s. 1 Evidence of repeat readings: at least two values of at least 5T. 1 1(c) Five sets of readings of d (different values) and time with correct trend (as d decreases, time decreases) and without help 4 from the Supervisor scores 4 marks, four sets scores 3 marks etc. Range: dmin ⩽ 9.5 cm. 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. d / cm , T / s , T 2 / s2. Consistency: 1 All values of raw d must be given to the nearest mm. Calculation: Values of T2 are correct. 1 1(d)(i) Axes: 1 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 the x and y directions. Axes must be labelled with the quantity that is being plotted. Scale markings must be no more than 2 cm (one large square) apart. 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 points in the table must be plotted (at least 4) on the grid for this mark to be awarded. Trend of points must be positive. It must be possible to draw a straight line that is within ± 1.0 cm (± 0.01 m) (to scale) on the d 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) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Candidates do not need to identify an anomalous point. However if there is a point off trend, it may be identified as anomalous by circling or labelling it. There must be at least 4 points left after one anomalous point is disregarded. Lines must not be kinked or thicker than half a small square. 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 matches graph drawn. 1(d)(iii) y-intercept: 1 Correct read-off from a point on the line and substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at d = 0, accurate to half a small square. 1(e) Value of A = candidate’s gradient and value of B = candidate’s intercept. 1 Values must not be written as fractions. Unit for A correct e.g. s2 cm–1 or s2 m–1 or s2 mm–1 and unit for B is s2. 1 1(f) g correctly calculated with a consistent unit. 1

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2 In this experiment, you will investigate the collision of two pendulums. (a) (i) ● Mould the two pieces of modelling clay onto the ends of the shorter strings to make two pendulums, as shown in Fig. 2.1. strings knot smaller piece of modelling clay larger piece of modelling clay Fig. 2.1 ● Set up the apparatus as shown in Fig. 2.2. stand clamp boss wooden blocks l larger piece of modelling clay bench Fig. 2.2 ● Adjust the modelling clay until the lengths of the pendulums are the same. ● The distance between the bottom of the wooden blocks and the centre of the smaller piece of modelling clay is l, as shown in Fig. 2.2. Measure and record l. l = ......................................................... [1] (ii) ● Hold the larger pendulum a short distance away from the smaller pendulum, as shown in Fig. 2.3. p Fig. 2.3 ● The horizontal distance between the centres of the pendulums is p. ● Hold the larger pendulum so that p is approximately 12 cm. ● Measure and record p. p = ......................................................... [1] (iii) Calculate R where p2 R = – 1 l 2. R = ......................................................... [1] (b) Justify the number of significant figures that you have given for your value of R. ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [1] (c) (i) ● Hold the larger pendulum so the horizontal distance between the centres of the pendulums is p. ● Release the larger pendulum so that the pendulums collide. ● After colliding, the maximum angle between the vertical and the string of the smaller pendulum is θ, as shown in Fig. 2.4. θ p Fig. 2.4 Measure and record θ. θ = ....................................................... ° [2] (ii) Estimate the percentage uncertainty in your value of θ. Show your working. percentage uncertainty = ......................................................% [1]

Mark scheme: 2(a)(i) Value of l to the nearest mm and final l ⩽ 25.0 cm with unit. 1 2(a)(ii) Final value of p with unit and in the range 11.0–13.0 cm. 1 2(a)(iii) 2 1 Correct calculation of −1 p  .  2   l  2(b) Justification for significant figures in R linked to significant figures in p and l. 1 2(c)(i) Values of raw given to the nearest degree and final in range 15–35. 1 Evidence of repeat values of . 1 2(c)(ii) Absolute uncertainty in in range 3–8. 1 If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if working is clearly shown. Correct method of calculation to find percentage uncertainty. 2(d) Second values of l and p. 1 Second value of . 1 Second value of is less than first value of . 1 2(e) Two values of k calculated correctly. The final k values must not be written as fractions. 1 2(f) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 10% leading to a consistent conclusion. 2(g)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B Difficulty measuring l with reason e.g. difficult to locate centre of clay/pendulum moves as rule touches it/clay has irregular shape/rule not vertical/parallax. C Difficulty with p with a reason e.g. difficult to locate centre of clay (credit only once in B or C)/ parallax error (credit only once in B or C)/p may change before release as hand moves/need to move eyes to look at protractor before release. D Difficulty measuring (max)  /angle with a reason e.g. protractor held in hand/hand moves while holding protractor/only achieved for a very short time/ difficult to judge or predict where maximum will be. E Difficulty with collision with reason e.g. inconsistency/twisting/shape/goes off at an angle/miss each other. 1 mark for each point up to a maximum of 4. 2(g)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). 4 B Improved method to measure l e.g. add a horizontal pointer or marker from the centre of the clay/clamp rule/detail of method to ensure rule is vertical. C Improved method to measure/ensure p has the same value in each experiment e.g. use of a stop or card gate. D Improved method for measuring e.g. clamp protractor or video/record/film with protractor in view. E Improved method e.g. use board to ensure flat surfaces of clay. 1 mark for each point up to a maximum of 4.

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