Cambridge A Level Physics 9702 — 2020 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate the equilibrium of a metre rule with a chain attached. (a) ● Attach the boss to the stand at a height of approximately 60 cm above the bench. ● Assemble the apparatus as shown in Fig. 1.1 with the nail held securely in the boss. ● Attach one end of the chain of paper clips to the string loop and allow the other end of the chain to rest on the bench. ● Attach the piece of adhesive putty to the metre rule approximately 40 cm from the nail. piece of adhesive x string loop putty boss metre rule chain of θ nail paper clips plumb line stand bench Fig. 1.1 ● Measure and record the distance x between the nail and the centre of the piece of adhesive putty, as shown in Fig. 1.1. x = ................................................... cm [1] (b) Measure and record the angle θ between the metre rule and the plumb line, as shown in Fig. 1.1. θ = ....................................................... ° [1] (c) Vary x and measure θ until you have six sets of values of x and θ. Do not use values of x less than 15 cm. Record your results in a table. Include values of cos θ in your table. [10] (d) (i) Plot a graph of cos θ on the y-axis against x 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 θ and x are related by the equation cos θ = ax + b 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 raw x to the nearest mm and final value in range 38.0–42.0 cm. 1 1(b) Value of θ in range 60°–100°. 1 1(c) Six (or more) sets of readings of x and θ with correct trend and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. Values of x should be different and non-zero. 5 Range: xmin ⩽ 20.0 cm and xmax ⩾ 45.0 cm. 1 Column headings: Each column heading must contain a quantity, a separating mark and a unit where appropriate. Heading for cosθ must have no unit. The presentation of quantity and unit must conform to accepted scientific convention e.g. x / cm. 1 Consistency: All values of raw θ must be given to the nearest degree. 1 Significant figures: Values of cosθ should be to the same number of s.f. as (or one more than) the number of s.f. in the corresponding value of θ. 1 Calculation: Values of cosθ calculated correctly. 1 Question Answer Marks 1(d)(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. Scales 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 must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square. 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. Trend of points should be correct. Scatter of plotted points must be no more than ±0.05 from a straight line on the cosθ axis. 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 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, e.g. not Δx / Δy. The sign of the gradient must match the 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 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 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. Values must not be written as fractions. 1 Unit for a correct (e.g. cm–1) and consistent with value and no unit given for b. 1

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2 In this experiment, you will investigate the motion of a roller on an inclined surface. (a) You are provided with a roller made from a bolt and two washers, as shown in Fig. 2.1. larger washer x smaller washer bolt nut nut nut Fig. 2.1 (i) Measure and record the distance x between the two lower faces of the washers, as shown in Fig. 2.1. x = ......................................................... [1] (ii) Measure and record the diameter D of the larger washer and the diameter d of the smaller washer. D = ............................................................... d = ............................................................... [1] (iii) Calculate L, where x D L = . (D – d ) L = ......................................................... [1] (iv) Justify the number of significant figures you have given for your value of L. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (b) ● Place the flat board on the bench and support the board with the wooden block so that the board is at an angle θ of approximately 10° to the bench, as shown in Fig. 2.2. flat board wooden block θ bench Fig. 2.2 ● Measure and record θ. θ = ............................................................. ° (i) ● Place the roller on the board as shown in Fig. 2.3 and wait until it is stationary. Fig. 2.3 ● Push the roller to one side and release it. The roller will oscillate. ● Take measurements to find the period T of the oscillations. T = ...................................................... s [2] (ii) Estimate the percentage uncertainty in your value of T. Show your working. percentage uncertainty = ......................................................... [1] (c) ● Use the spanners to loosen the two nuts either side of the smaller washer. ● Move these nuts and the smaller washer along the bolt until x is as large as possible. Use the spanners to tighten the nuts. ● Repeat (a)(i), (a)(iii) and (b)(i). x = ............................................................... L = ............................................................... T = ............................................................ s [2]

Mark scheme: 2(a)(i) Value of raw x to nearest mm and final value in range 20–24 mm with unit. 1 2(a)(ii) Values of raw D and d to nearest mm and final value of D in the range 38–42 mm. 1 2(a)(iii) Correct calculation of L. 1 2(a)(iv) Justification based on significant figures in x, D and (D – d). 1 2(b)(i) Raw values of times all to 0.1 s or all to 0.01 s and value of T in range 0.5–2.5 s. 1 Evidence of repeats: at least two values of time. 1 2(b)(ii) Percentage uncertainty based on an absolute uncertainty in time value of 0.2–0.5 s. 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(c) Second values of x and T. 1 Quality: second T > first T. 1 2(d)(i) Two values of k calculated correctly. The final values of k must not be fractions. 1 2(d)(ii) Valid comment relating to the calculated values of k, testing against a criterion specified by the candidate. 1 2(e) Correct calculation of g. 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 diameters or x with reason e.g. parallax/zero not at end of ruler/x varies around roller/nuts or bolt prevent placement of ruler. C θ small so large uncertainty/large % uncertainty in θ. D Oscillations die away quickly. E Difficult to measure time/T because it is difficult to judge the end/beginning/completion of an oscillation. F Roller slips down board. 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 Use metre rule/calipers/micrometer/blocks either side of washer/use pointers with detail. C Method to reduce uncertainty in θ e.g. use of trigonometry with detail/increase θ. D Method to increase the number of oscillations e.g. smoother board/named smooth material for board/sand board. E Method of improving timing e.g. fiducial marker at centre of oscillation or video/record/film with timer/frame-by-frame. F Method of reducing slipping e.g. rougher/named higher friction surface/smaller θ. 1 mark for each point up to a maximum of 4. 4

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