Cambridge A Level Physics 9702 — 2021 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will investigate the oscillations of a metre rule. (a) ● Set up the apparatus as shown in Fig. 1.1, with the scales on the metre rules facing upwards. stand adhesive jaws of putty adhesive clamp upper rule boss putty string loop H string loop lower rule w w bench Fig. 1.1 ● Adjust the clamp so that the upper rule is parallel to the bench. ● Adjust the positions of the string loops so that each loop is approximately 40 cm from the nearest ends of the two rules. ● The vertical distance between the two rules is H. Measure and record H. H = ......................................................... [1] (b) ● For both rules, the distance between the 50 cm mark and each string loop is w, as shown in Fig. 1.1. Adjust the positions of the string loops until the distances w are equal and approximately 10 cm. ● Measure and record w. w = ......................................................... cm ● Gently rotate the lower rule and release it. The lower rule will oscillate as shown in Fig. 1.2. lower rule upper rule lower rule TOP VIEW Fig. 1.2 ● Take measurements to determine the period T of the oscillations. T = ............................................................ s [2] (c) Vary w in the range 5.0 cm G w G 20.0 cm and determine six sets of readings of w and T. 1 Record your results in a table. Include values of in your table. w [9] 1(d) (i) Plot a graph of T on the y-axis against on the x-axis. [3] w (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient of this line. gradient = ......................................................... [1] (e) (i) It is suggested that the quantities T and w are related by the equation B T = w where B is a constant. Using your answer to (d)(iii), determine a value for B. Give an appropriate unit. B = ......................................................... [2] (ii) It is suggested that B is given by the equation 3π2H3 B2 = g where g is the acceleration of free fall. Using your answers to (a) and (e)(i), determine a value for g. g = ................................................ m s–2 [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of H with unit and in the range 20.0–40.0 cm. 1 1(b) Final value of T in the range 2.0–10.0 s. 1 At least two measurements of nT where n ⩾ 5. 1 1(c) Six (or more) sets of readings of w (different values) and time with the correct trend and without help from the Supervisor scores 4 marks, five sets scores 3 marks, etc. 4 Range: wmin ⩽ 6.0 cm and wmax ⩾ 18.0 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. T / s and 1 / w / cm–1 or 1 / w (1 / cm). 1 Consistency: All values of w must be given to the nearest 0.1 cm. 1 Significant figures: All values of 1 / w must be given to the same number of s.f. as (or one more than) the number of s.f. of raw w. 1 Calculation: Values of 1 / w are correct. 1 Question Answer Marks 1(d)(i) Axes: Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). 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 (at least 5) must be plotted on the grid. Trend of points on graph must be correct. It must be possible to draw a straight line that is within ± 0.01 cm–1 (or ± 1 m–1) on the 1 / w axis of all plotted points. 1 1(d)(ii) Line of best fit: Judge by the 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 (i.e. circled or labelled) by the candidate. There must be at least five points left after the anomalous point is disregarded. Line 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. Both read-offs must be accurate to half a small square in both the x and y directions. Method of calculation must be correct, e.g. Δy / Δx. Gradient sign on answer line matches graph drawn. 1 1(e)(i) B = candidate’s gradient value. Value must not be written as a fraction. 1 Unit for B correct (e.g. cm s or m s). 1 1(e)(ii) Correct calculation of g consistent with the unit. 1

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2 In this experiment, you will determine the weight of a metre rule. (a) (i) ● Attach the spring to the clamp. ● Suspend the mass hanger from the spring as shown in Fig. 2.1. clamp boss spring L0 mass hanger stand bench Fig. 2.1 ● The length of the coiled section of the spring is L0. Measure and record L0. L0 = .................................................... cm [1] (ii) Estimate the percentage uncertainty in your value of L0. Show your working. percentage uncertainty = ......................................................... [1] (b) (i) ● Add an additional mass of 0.100 kg to the mass hanger. ● The new length of the coiled section of the spring is L1. Measure and record L1. L1 = ......................................................... cm ● Remove the 0.100 kg mass. [1] (ii) Calculate (L1 – L0). (L1 – L0) = ................................................... cm [1] (iii) The spring constant k is given by the equation F k = (L1 – L0) where F is 0.981 N. Calculate k. k = ......................................................... [1] (iv) Justify the number of significant figures that you have given for your value of k. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (c) (i) ● Set up the apparatus as shown in Fig. 2.2. L stand adhesive putty d metre rule Fig. 2.2 ● Support the rule on the mass hanger. You may need to use some of the adhesive putty to stop the rule from slipping off the mass hanger. ● The distance between the lower end of the rule and the mass hanger is d, as shown in Fig. 2.2. The length of the coiled section of the spring is L. Adjust the apparatus so that d is approximately 90 cm and the spring is vertical. ● Measure and record d and L. d = ......................................................... cm L = ......................................................... cm ● Using your answer to (a)(i), calculate (L – L0). (L – L0) = ......................................................... cm [1] (ii) Repeat (c)(i) with a distance d of approximately 60 cm. d = ......................................................... cm L = ......................................................... cm (L – L0) = ......................................................... cm [2]

Mark scheme: 2(a)(i) L0 in the range 3.0–8.0 cm. 1 2(a)(ii) Percentage uncertainty based on an absolute uncertainty ΔL0 in the range 2–5 mm. 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. 1 2(b)(i) Value of L1 > L0. 1 2(b)(ii) Correct calculation of (L1 – L0). 1 2(b)(iii) Correct calculation of k. 1 2(b)(iv) Justification of the number of significant figures linked to the number of significant figures in F and (L1 – L0). 1 2(c)(i) Raw value(s) of d and L recorded to the nearest millimetre. 1 2(c)(ii) Second values of d and L. 1 Second value of (L1 – L0) is larger than the first value of (L1 – L0). 1 2(d)(i) Two values of C calculated correctly. The final values must not be written as fractions. 1 2(d)(ii) Valid comment consistent with the calculated values of C, testing against a criterion stated by the candidate. 1 2(e) Correct calculation of W. 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 measure d with reason, e.g. rule falls/rule slips off/end point near mass hanger difficult to identify. C Values of (L – L0) or (L1 – L0) are small giving large uncertainty (error) or large percentage uncertainty (error) in (L – L0) or (L1 – L0). D Problem with mass of putty, e.g. mass of putty not included/putty changes force on spring. E Difficulty to judge whether spring is vertical/to make spring vertical. F Difficult to measure L0, L, L1 or length of spring with reason, e.g. holding rule to measure length nudges spring/coils slanted/rule not vertical/parallax/hands unsteady. G k determined using only one result. 1 mark for each point up to a maximum of 4. 4 Question Answer Marks 2(f)(ii) A Take more readings and plot a graph or take more readings and compare C values (not “repeat readings” on its own). B Method to improve measurement of d, e.g. string loop under mass hanger to hold rule. C Use of named device for more precise length measurements, e.g. calipers/travelling microscope. D Improved method to account for mass of putty, e.g. use a balance to measure mass of putty/use glue/use tape (instead of putty). E Method to provide a vertical reference, e.g. use a plumb-line behind spring/set square on bench large enough to be viewed behind spring/method to ensure metre rule is vertical with set square on bench. F Improved method to measure L0, L, L1 or length of spring, e.g. pointers on rule/clamped ruler/mark points on spring coils for reference. G Method to improve determination of k, e.g. take many readings and plot graph/use a range of masses/many readings and calculate average. 1 mark for each point up to a maximum of 4. 4

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