Cambridge A Level Physics 9702 — 2011 May/June Paper 3 · Variant 5

1 In this experiment you will investigate how the motion of two pendulums depends on the tension in a spring connecting them. (a) Measure and record the unstretched length l of the coiled part of the spring as shown 0 in Fig. 1.1. l0 Fig. 1.1 l = ..................................................[1] 0 (b) (i) Set up the apparatus as shown in Fig. 1.2. loop of string over rod of clamp spring 50 cm bob A bob B at least 5 cm bench Fig. 1.2 (ii) Position the stands so that the coiled part of the spring has approximate length l + 2 cm (so that the spring is extended by approximately 2 cm). 0 (iii) Measure and record the length l of the coiled part of the spring. For Examiner’s Calculate the extension x of the spring, where x = l – l 0. Use l = ...................................................... x = ...................................................... (iv) Gently pull bob A towards you. Release the bob and watch the movement of the two bobs. Bob A will eventually stop and start moving again. It will then stop for a second time. Determine and record the time T between these two stops. T = ..................................................[2] (c) By moving the stands further apart, repeat (b)(iii) and (b)(iv) until you have six sets of For readings of l, x and T, with x in the range 2 cm x 10 cm. Examiner’s Use [9] (d) (i) Plot a graph of T 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] For Examiner’s Use (e) It is suggested that the quantities T and x are related by the equation For Examiner’s T = px + q Use where p and q are constants. Use your answers in (d)(iii) to determine the values of p and q. Give appropriate units. p = ...................................................... q = ...................................................... [1] (f) Use your values in (e) to determine the extension x that would be expected to give a value of T = 75 s. x = ..................................................[1] You may not need to use all of the materials provided. For Examiner’s Use

Mark scheme: 1 (a) Value of l0 with unit in range 1.5 cm l0 3.0 cm. [1] (b) (iv) Value of T with unit 20 s T 5 s. [1] Evidence of repeat times. (c) Six sets of readings of l and T scores 4 marks, five sets scores 3 marks etc. [4] Incorrect trend then –1 Help from supervisor –1. Range : ∆x ≥ 7 cm. [1] Column headings: [1] Each column heading must contain a quantity and a unit where appropriate. There must be some distinguishing mark between the quantity and the unit e.g. T / s, x / cm. Precision of x from raw values of l and l0. [1] Check values of x the same as the least precision in l or l0. [1] (d) (i) Axes: [1] Sensible scales must be used. Awkward scales (e.g. 3:10) are not allowed. Scales must be chosen so that the plotted points on the grid occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity which is being plotted. Ignore units. Scale markings should not be more than three large squares apart. Plotting of points: [1] All observations in table must be plotted. Write a ringed total of plotted points ignoring any point off the grid. Check points plotted correctly. Tick if correct. Re-plot if incorrect. Work to an accuracy of half a small square. Do not accept ‘blobs’ (points with diameter greater than half a small square). Quality: [1] All points in the table must be plotted (at least five) for this mark to be scored. Judge by scatter of all points about straight line. All points must be within 4 mm to scale from a straight line. Indicate tolerance on graph. Indicate reason if mark is not awarded. (ii) Line of best fit: [1] Judge by the balance of all the points (at least five) about candidates’ line. There must be an even distribution of points either side of the line along the whole length. If mark is not awarded indicate rotation or direction of best fit line. Lines must not be kinked. (iii) Gradient: [1] The hypotenuse of the triangle must be at least half the length of the drawn line. Read-offs must be accurate to half a small square. Check for ∆y/∆x (i.e. do not allow ∆x/∆y). If incorrect, write in the correct value(s). y-intercept: [1] Either: check correct read off from a point on the line and substitute into y = mx + c. Read off must be accurate to half a small square. Allow ecf of gradient value. GCE A LEVEL – May/June 2011 9702 35 Or: check read-off of intercept directly from graph. (e) p is the value of the candidate’s gradient in s m–1 , s cm–1 , s mm–1 , mm–1 s. [1] q is the value of the candidate’s y-intercept in s. (f) Value of x (10 – 100 cm) with consistent unit when T = 75 s. [1] Correct method seen. [Total: 20]

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2 In this experiment you will drop a mass onto a rod standing in sand and investigate the distance that the rod moves into the sand. (a) You have been provided with two wooden rods of different diameters. Measure and record the diameter d of the thicker rod. d = ..................................................[2] (b) Flatten the surface of the sand. Stand the rod vertically in the sand up to the mark drawn on the rod, as shown in Fig. 2.1. wooden rod sand mark on rod container Fig. 2.1 (c) (i) Hold the mass hanger so that the distance h between its bottom and the top of the For rod is approximately 10 cm. Examiner’s The centre of the bottom of the mass hanger should be vertically above the wooden Use rod, as shown in Fig. 2.2. mass hanger h wooden rod sand Fig. 2.2 (ii) Measure and record the height h. h = ..................................................[1] (d) (i) Drop the mass hanger from this height h above the rod. (ii) Without making a further mark on the rod, determine the new length x of the rod below the surface of the sand, as shown in Fig. 2.3. x Fig. 2.3 x = ..................................................[1] (iii) Calculate and record the change in depth y of the rod in the sand as a result of the For impact of the mass hanger. Examiner’s Use y = ..................................................[1] (e) Estimate the percentage uncertainty in your value of y. percentage uncertainty = ..................................................[1] (f) Using the thinner rod repeat (a), (b), (c)(i), and (d). Use the same value of h as in (c)(ii). d = ....................................................... x = ...................................................... y = ...................................................... [3]

Mark scheme: 2 (a) Measurement of d to nearest 0.01 mm with consistent unit. [1] Evidence of repeat readings. (c) (ii) Value of h in the range 9 cm – 11 cm with unit. [1] (d) (ii) Value of x in the range 1 cm – 5 cm to the nearest mm with unit. [1] (iii) Value of y = x – (10 ± 2) mm. [1] (e) Absolute uncertainty in y in range 2 – 5 mm (or half the range of repeated readings). [1] Correct calculation to get percentage uncertainty. (f) Second value of d < (a). [1] Second value of x. [1] Quality : second value of y > first value of y. [1] (g) (i) Values of k calculated correctly. [1] (ii) Sensible comment relating to the calculated values of k, testing against a specified criterion. [1] (iii) Justification of s.f. in k linked to least s.f. in d and y or x. [1] GCE A LEVEL – May/June 2011 9702 35 (h) (i) Limitations 4 max (ii) Improvements 4 max Do not credit Ap Two readings (of d and l) not enough/ As Take more readings and plot a Take more only two readings/too few readings. graph/more values of k (and readings and compare). calculate average k / only one reading. Bp Maintaining h constant. Bs Clamp mass hanger/specified release mechanism/hold against fixed pointer. Cp Explain difficulty in getting Cs Put mark on rod/use a clip/ measurement of x/depth accurately measure rod out of sand with scale with finger/position of finger and line or ruler/scale marked on ruler/draw may not be in line. mark all the way round. Dp Rod falls sideways/not entering sand Ds Practical method to keep rod vertically. vertical e.g. guide for rod. Ep Cannot see if mass is directly above Es Practical method to ensure Do not credit rod. centralisation of mass e.g. guide for use of mass. computers, assistants, dataloggers. Fp Depth/x very small Fs Increase height/mass Xp Specific problem candidate Xs e.g. solution to specific problem Ignore encountered e.g. uniformity of sand. candidate encountered. uneven surface. [Total: 20]

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