Cambridge A Level Physics 9702 — 2019 Feb/March Paper 3 · Variant 3

1 In this experiment, you will investigate a pendulum with a mass fixed at each end. (a) • Assemble the apparatus with the nail passing through the third hole from C, as shown in Fig. 1.1. • Ensure that the nail is held securely in the clamp. mass stand wooden strip clamp holes boss x c mark labelled C nail (held in clamp) bench Fig. 1.1 • The distance between the nail and C is x, as shown in Fig. 1.1. Measure and record x. x = .................................................... cm [1] (b) • Push the bottom of the strip horizontally through a distance of approximately 5 cm. Release the strip so that it oscillates. • Determine the period T of these oscillations. T = ....................................................... s [2] (c) Change x by positioning the nail in a different hole and repeat (b). Repeat until you have six sets of values of x and T. 1 2 Record your results in a table. Include values of and T in your table. x [9] 2 1(d) (i) Plot a graph of T on the y-axis against on the x-axis. [3] x (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 x are related by the equation 2 a T = + b x where a and b are constants. Use your answers in (d)(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) value of x to nearest mm and in range 4.5 to 5.5 cm 1 1(b) value of T in range 1.50 s to 2.50 s 1 repeat readings – at least two values of at least 5T 1 1(c) six sets of readings of x and T with correct trend and without help from supervisor scores 4 marks, five sets scores 3 marks etc. 4 range: xmin ⩽ 2.5 cm and xmax ⩾ 13.5 cm 1 column headings: each column heading must contain a quantity and a unit the presentation of quantity and unit must conform to accepted scientific convention. e.g. T 2 / s2 1 consistency: all values of raw times must be given to the nearest 0.1 s or all values to the nearest 0.01 s 1 significant figures: significant figures for every value of 1 / x same as, or one greater than, the s.f. of x as recorded in table 1 calculation: values of 1 / x calculated correctly 1 Question Answer Marks 1(d)(i) axes: sensible scales must be used, no awkward scales (e.g. 3:10) scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions scales must be labelled with the quantity which is being plotted scale markings should be no more than 3 large squares apart 1 plotting of points: all observations must be plotted on the grid diameter of plotted points must be ⩽ half a small square (no blobs) plots must be accurate to within half a small square in both x and y directions 1 quality: all points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of plots must be no more than ± 0.05 cm–1 from a straight line in the 1 / x direction 1 1(d)(ii) line of best fit: judged by balance of all points on the grid (at least 5) about the candidate’s line. There must be an even distribution of points either side of the line along the full length one anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate lines must not be kinked or thicker than half a small square 1 1(d)(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 both read-offs must be accurate to half a small square in both the x and y directions 1 y-intercept: Either correct read-off from a point on the line substituted into y = mx + c or an equivalent expression, with read-off accurate to half a s square in both x and y directions Or intercept read directly from the graph, with read-off at x = zero accurate to half a small square in y direction 1 Question Answer Marks 1(e) a equal to candidate’s gradient, and b equal to candidate’s intercept, and values are not written as fractions 1 unit for a is correct and consistent with value unit for b is correct 1

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2 In this experiment, you will investigate the relationship between the pressure in a balloon and its diameter. (a) • You are provided with two partially inflated balloons. Place the larger balloon on the bench with its neck at the side, as shown in Fig. 2.1. • Put pieces of modelling clay around the balloon to stop it rolling, as shown in Fig. 2.1. balloon modelling B clay tray bench Fig. 2.1 • The diameter of the balloon is B, as shown in Fig. 2.1. Measure and record B. B = ......................................................... [1] (b) • Wet a small area on the top of the balloon with a damp paper towel. • Balance the transparent block on the top of the balloon, as shown viewed from above in Fig. 2.2. tape handle transparent block Fig. 2.2 • The contact patch will be visible, as shown in Fig. 2.3. d contact patch Fig. 2.3 • The diameter of the contact patch is d, as shown in Fig. 2.3. Measure and record d. d = ......................................................... [2] (c) Estimate the percentage uncertainty in your value of d. percentage uncertainty = ......................................................... [1] (d) Calculate the pressure P in the balloon using the relationship 4mg P = πd 2 where g = 9.81 N kg–1 and m is the mass of the transparent block written on the card. P = ............................................... Nm–2 [2] (e) Justify the number of significant figures you have given for your value of P. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... [1] (f) Repeat (a), (b) and (d) using the smaller partially inflated balloon. B = ............................................................... d = ............................................................... P = ..................................................... Nm–2 [3]

Mark scheme: 2(a) value for B, with unit 1 2(b) measured value(s) for d, with unit, to nearest mm 1 evidence of repeat readings 1 2(c) absolute uncertainty in d value ⩾ 0.2 cm and correct method of calculation to obtain percentage uncertainty. if several readings have been taken, then the absolute uncertainty can be half the range if the working is clearly shown (but not zero if values are equal) 1 2(d) calculation of P correct 1 POT of P value matches unit 1 2(e) justification based on s.f. in d, m and g 1 2(f) value for second B 1 value for second d 1 Quality: d smaller for smaller B 1 2(g)(i) two values of k calculated correctly 1 2(g)(ii) sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate 1 Question Answer Marks 2(h)(i) two k values are not enough to draw a valid conclusion 4 max difficult to measure B with reason, e.g. pressing on balloon / ruler scale doesn’t start at zero / parallax difficult to balance Perspex block on balloon / balloon kept moving difficult to measure d with reason, e.g. not circular / changes when block touched / parallax / refraction changes apparent size difficult to see (edges of) contact patch (clearly) 2(h)(ii) take more readings and plot a graph / calculate more k values and compare 4 max workable method of reducing parallax for B e.g. callipers fix balloon in place with tape / glue / Blu-tack / trap between blocks at sides grid on block / travelling microscope / thinner block use contrasting colours for balloon and liquid

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