Cambridge A Level Physics 9702 — 2013 May/June Paper 3 · Variant 1

1 In this experiment, you will investigate a system in equilibrium due to several turning forces. (a) Measure and record the distance L between the two holes in the wooden strip as shown in Fig. 1.1. L wooden strip loop of string Fig. 1.1 L = ............................................. m [1] (b) Write down the mass M given on the card. M = ................................................. kg (c) (i) Set up the apparatus as shown in Fig. 1.2, with mass m = 0.040 kg. For Examiner’s Use stand d rod of clamp in boss loop of string wooden strip mass M mass m bench Fig. 1.2 (ii) Adjust the position of the wooden strip until it balances. Measure and record the distance d, as shown in Fig. 1.2. d = ............................................. m [1] (d) Vary m and repeat (c)(ii) until you have six sets of readings of m and d. For Examiner’s 1 Use Include values of in your table. d [10] 1 (e) (i) Plot a graph of on the y-axis against m on the x-axis. [3] d (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 (f) The quantities d and m are related by the equation For Examiner’s 1 Use = P m + Q d where P and Q are constants. Using your answers in (e)(iii), determine the values of P and Q. Give appropriate units. P = ...................................................... Q = ...................................................... [1] (g) The constant P is related to L and M by 1 P = kML where k is a constant. Using your answers in (a), (b) and (f), calculate a value for k. You need not include units for k. k = ..................................................[1] You may not need to use all of the materials provided. For Examiner’s Use

Mark scheme: 1 (a) Value of L in the range 0.790–0.810 m. [1] (c) (ii) Value of d to the nearest mm and d < 0.600 m. [1] (d) Six sets of readings of m and d scores 5 marks, five sets scores 4 marks etc. [5] Correct trend is d decreases as m increases. Help from Supervisor –1. Range of m: mmin = 0 g or 10 g; mmax > 100 g. [1] Column headings: [1] Each column heading must contain a quantity and a unit. The presentation of quantity and unit must conform to accepted scientific convention e.g. 1/d /m–1. Consistency: [1] All values of d must be given to the nearest mm. Significant figures: [1] Significant figures for every row of values of 1/d same as, or one greater than, d as recorded in table. Calculation: [1] Values of 1/d calculated correctly. (e) (i) Axes: [1] 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 that is being plotted. Scale markings should be no more than three large squares apart. Plotting of points: [1] All observations in the table must be plotted. Diameter of plotted points must be ≤ half a small square (no “blobs”). Work to an accuracy of half a small square. Quality: [1] All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of points must be less than ± 0.05 m–1 of 1/d from a straight line. (ii) Line of best fit: [1] Judge by 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. Line must not be kinked or thicker than half a small square. GCE AS/A LEVEL – May/June 2013 9702 31 (iii) Gradient: [1] The hypotenuse of the triangle must be at least 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. The method of calculation must be correct. y–intercept: [1] Either: Correct read-off from a point on the line and substituted into y = mx + c. Read-off must be accurate to half a small square in both x and y directions. Or: Correct read-off of the intercept directly from the graph. (f) Value of P = candidate’s gradient. Value of Q = candidate’s intercept. Unit for P (e.g. kg–1 m–1) and Q (m–1). [1] (g) Value of k in range 1.0–2.0. [1] [Total: 20]

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2 In this experiment, you will investigate the motion of a wooden rod supported by a string. (a) (i) Set up the apparatus as shown in Fig. 2.1 with height h approximately 40 cm. 10 cm boss clamp short wooden rod string e stand h long wooden rod bracket nail bench Fig. 2.1 The short wooden rod should be held firmly in the clamp. Place the bracket on the base of the stand and rest the head of the nail in the centre of the bracket. (ii) Measure and record the angle θ between the string and the long wooden rod as For shown in Fig. 2.1. Examiner’s Use θ = ..................................................[2] (iii) Estimate the percentage uncertainty in your value of θ. percentage uncertainty = ..................................................[1] (iv) Calculate sin θ. sin θ = ..................................................[1] (b) Gently displace the end of the long wooden rod to the left as shown in Fig. 2.2 (top For view). Examiner’s Use bracket nail short wooden rod clamp top view string long wooden rod one complete swing Fig. 2.2 Release the rod and watch the movement. The rod will move to the right and back towards the left, completing a swing. The time taken for one complete swing is T. By timing several of these complete swings, determine an accurate value for T. T = ..................................................[2]

Mark scheme: 2 (a) (ii) Value of θ with unit. Help from Supervisor –1. [1] θ in range 72°–92°. [1] (iii) Absolute uncertainty in θ in range 2º–10º. If repeated readings have been taken, then the uncertainty can be half the range (but NOT zero if values are equal). Correct method of calculation to obtain percentage uncertainty. [1] (iv) Correct calculation of sin θ. Ignore unit. Do not allow sin θ = O/H ideas as triangle not a right-angled triangle. [1] (b) Value of T with unit in range 1.0 ≤ T ≤ 2.0 s. [1] Evidence of repeats here or in (c)(ii). [1] (c) (ii) Second value of θ. [1] Second value of T. [1] Second value of T < first value of T. [1] (d) (i) Two values of k calculated correctly. [1] (ii) Justification of s.f. in k linked to significant figures in T (or t) and θ. [1] (iii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] GCE AS/A LEVEL – May/June 2013 9702 31 (e) (i) Limitations max. 4 (ii) Improvements max. 4 Do not credit A two readings not enough (to draw a take more readings and plot a “repeat readings” conclusion) graph/ on its own calculate more k values and /few readings/only compare one reading /take more readings and (calculate) average k B end of nail slips in bracket/bracket use something with a sharper method of fixing nail moves/is not stable point e.g. cocktail stick/dent in bracket (to seat head of nail) valid method to fix bracket e.g. use blu-tack/glue/use bigger/heavier bracket/fix bracket/ clamp to bench C difficult to measure T with reason ‘too few oscillations’ e.g. heavily damped/oscillations die on its own/ away quickly T small D difficult to judge start of/end use a fixed/fiducial marker human error/ of/complete oscillation /improved timing method e.g. reaction time video with timer/video and view /record time for frame-by-frame more oscillations multiflash photography with marker fixed to rod strobe rate /marker placed at extreme of oscillation use light gate E difficult to read θ/angle/protractor clamp protractor parallax error with reason e.g. difficult to hold steady in the air use a larger protractor F fans/air conditioning affect oscillations [Total: 20]

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