Cambridge A Level Physics 9702 — 2022 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will investigate the balancing of a metre rule. (a) ● Set up the apparatus as shown in Fig. 1.1. stand clamp boss upper string loop upper spring L0 lower spring lower string loop bench Fig. 1.1 ● The length L0 of the spring combination is measured between the top coil of the upper spring and the bottom coil of the lower spring, as shown in Fig. 1.1. Measure and record L0. L0 = ......................................................... cm ● Use the lower string loop to suspend a total mass of 200 g, as shown in Fig. 1.2. L mass hanger mass Fig. 1.2 ● The new length of the spring combination is L. Measure and record L. L = ......................................................... cm ● The spring constant k of the spring combination is given by the equation W k = (L – L0) where W is 1.96 N. Calculate k. k = ............................................................... [2] (b) ● Set up the apparatus as shown in Fig. 1.3. pivot L a metre rule 50.0 cm 95.0 cm Fig. 1.3 ● Use the adhesive putty to fix two 100 g slotted masses with their centres above the 50.0 cm mark on the rule. The masses must remain at this position throughout the experiment. ● Place the lower string loop at the 5.0 cm mark on the rule. ● The distance between the pivot and the midpoint of the rule is a. Adjust the pivot so that a is approximately 25 cm. ● Adjust the stand, boss and clamp so that the springs are vertical and the rule is horizontal. ● Measure and record a and L. a = ............................................................... L = ............................................................... ● The extension of the spring combination is given by the equation e = L – L0. Calculate e. e = ............................................................... ● Change a by moving the pivot. Adjust the stand, boss and clamp so that the springs are vertical and the rule is horizontal. Measure a and L. Repeat until you have six sets of values of a and L. Do not include values of a less than 15.0 cm. 1 1 Record your results in a table. Include values of e, and in your table. a e [9] 1 1(c) (i) Plot a graph of on the y-axis against on the x-axis. [3] e a (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ............................................................... y-intercept = ............................................................... [2] (d) (i) It is suggested that the quantities e and a are related by the equation 1 1 = B + C e a where B and C are constants. Using your answers in (c)(iii), determine the values of B and C. Give appropriate units. B = ............................................................... C = ............................................................... [2] (ii) Theory suggests that k C = (R + W) where R is the weight of the rule and W is 1.96 N. Using your answers in (a) and (d)(i), determine a value for R. R = ..................................................... N [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: Question Answer Marks 1(a) Value(s) of raw L to the nearest mm. 1 Correct calculation of k. 1 1(b) Six sets of readings of a (different values) and L with the correct trend (L increases as a increases) and without help from 4 the Supervisor scores 4 marks, five sets scores 3 marks etc. Range: amin ⩽ 20.0 cm and amax ⩾ 40.0 cm. 1 Column headings: 1 Each column heading must contain a quantity and a unit where appropriate. 1 1 1 The presentation of quantity and unit must conform to accepted scientific convention e.g. / m–1, (cm–1), / 1 / cm. a a e Consistency: 1 All values of a must be given to the nearest 0.1 cm. Significant figures: 1 1 All values of must be given to the same number of s.f. as (or one more than) the number of s.f. in the raw a values. a 1 1 Calculation: Values of calculated correctly. e 1(c)(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 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 5) on the grid for this mark to be awarded. Trend of points must be positive. 1 It must be possible to draw a straight line that is within  0.005 cm–1 ( 0.500 m–1) on the axis (normally x-axis) of all a plotted points. 1(c)(ii) Line of best fit: 1 ‘Best fit’ is judged by the 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. 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 5 points left after one anomalous point is disregarded. Lines must not be kinked or thicker than half a small square. 1(c)(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. 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 1 Intercept read directly from the graph, with read-off at = 0, accurate to half a small square. a 1(d)(i) Value of B = candidate’s gradient value and value of C = candidate’s y-intercept value. 1 Values must not be written as fractions. B has no unit and unit for C (mm–1 or cm–1 or m–1) correct. 1 1(d)(ii) Correct calculation of R. 1

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2 In this experiment, you will investigate the oscillations of a triangular card. (a) ● Determine the midpoint M of the shortest side of the triangle. ● Draw a line from M to the opposite corner of the triangle, as shown in Fig. 2.1. M Fig. 2.1 (not to scale) ● Determine the midpoint N of one of the longer sides. ● Draw a line from N to the opposite corner of the triangle, as shown in Fig. 2.2. N C M Fig. 2.2 (not to scale) ● Mark the point C where the two lines cross. ● The distance between C and M is d. Measure and record d. d = ..................................................... m [1] (b) (i) ● On the line from M to the opposite corner, mark a point P a distance of approximately 0.06 m from C, as shown in Fig. 2.3. P N p C M Fig. 2.3 (not to scale) ● The distance between C and P is p, as shown in Fig. 2.3. Measure and record p in metres. p = ........................................................... m ● Place the card on the cork so that P is above the cork. Use the pin to carefully pierce a small hole in the card at P. ● Set up the apparatus as shown in Fig. 2.4. stand pin through P boss C cork triangle clamp bench Fig. 2.4 ● Displace the base of the triangle through a small distance to the side. Release it so that it oscillates as shown in Fig. 2.5. C Fig. 2.5 ● Take measurements to determine the period T of the oscillations. T = ............................................................ s [3] (ii) Estimate the percentage uncertainty in your value of T. Show your working. percentage uncertainty = ..................................................... % [1] (iii) Calculate p2 and T2p. p2 = ............................................................... T2p = ...............................................................

Mark scheme: 2(a) Final d value to the nearest mm and raw d to nearest mm and in the range 0.068–0.072 m. 1 2(b)(i) p in the range 0.055–0.065 m. 1 All raw time measurements to the nearest 0.1 s or all to the nearest 0.01 s and final T in range 0.50 s ⩽ T ⩽ 1.00 s. 1 Repeats: At least two measurements of at least 2T. 1 2(b)(ii) Absolute uncertainty in nT in the range 0.2–0.4 s or absolute uncertainty in T in the range (0.2 / n) s to (0.4 / n) s where n is 1 the number of oscillations used. 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(b)(iii) Correct calculation of p2 and T2p. 1 2(b)(iv) Justification for significant figures in T2p correctly linked to significant figures in p and raw times. 1 2(b)(v) Second value of p and second value of T. 1 Second value of T larger than first value of T. 1 2(c) Two values of q calculated correctly. The final q values must not be written as fractions. 1 2(d) Calculation of percentage difference between candidate’s two q values. 1 Comparison of percentage difference with 15% leading to a consistent conclusion. 2(e) Correct calculation of g with correct unit (e.g. m s–2). 1 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B Difficulty linked to the card e.g. card is not flat/card bends (when making hole at P)/difficult to line up pin with P and cork and press without bending card. C Difficult to judge/decide/determine when to start and/or stop the stop-watch or when oscillation begins and/or ends. D Few/small number of oscillations or oscillations die quickly. E Oscillations not in one plane or card hits stand. 1 mark for each point up to a maximum of 4. 2(f)(ii) A Take more readings and plot a graph or take more readings and compare q values (not “repeat readings” on its own). 4 B Method to ensure card remains flat when making hole e.g. mat below triangle or use thicker/stiffer/heavier card. C1 Place a grid behind the apparatus or fiducial mark at the centre of the oscillation or plumb-line at centre. C2 Video/film/record with timer/frame-by-frame. D Use longer pin or named material which has less friction than cork or use larger hole. E Use thicker/stiffer/heavier card (award thicker/stiffer/heavier card only once as B or E) or turn off fans/air conditioning or use a wind-shield. 1 mark for each point up to a maximum of 4.

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