Cambridge A Level Physics 9702 — 2011 Oct/Nov Paper 3 · Variant 1

1 In this experiment you will investigate the equilibrium position of a metre rule with a mass attached to one end. (a) (i) Use a loop of string to balance the metre rule as shown in Fig. 1.1. rod of clamp loop of string metre rule mass k 30 cm bench Fig. 1.1 (ii) Measure and record distance k between the loop and the end of the rule as shown in Fig. 1.1. k = ........................................... cm [1] (b) (i) Use the other loop of string to attach the mass hanger at a distance d from the end For of the rule as shown in Fig. 1.2. The value of d should be approximately 5 cm. Examiner’s Use (ii) For this value of d, adjust the position of the rule so that it balances. The new distance between the first loop and the end of the rule is D, as shown in Fig. 1.2. D d loop of string loop of string mass hanger Fig. 1.2 (iii) Measure and record lengths d and D. d = ...................................................... D = ...................................................... [1] (D – d ) (iv) Calculate the value of . D (D – d ) = ...................................................... D (c) By moving the mass hanger along the metre rule, repeat (b)(ii), (b)(iii) and (b)(iv) until For you have six sets of values of d and D. Examiner’s 1 (D – d ) Use Include values of and in your table. D D [10] (D – d ) 1 (d) (i) Plot a graph of on the y-axis against on the x-axis. [3] D 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 (e) The quantities d and D are related by the equation For Examiner’s (D – d ) A Use = – B D D where A and B are constants. A Use your answers in (d)(iii) to determine the value of B. Give appropriate units. A = ..................................................[2] B You may not need to use all of the materials provided. For Examiner’s Use

Mark scheme: 1 (a) (ii) Value of k in range: 50 cm ≤ k ≤ 100 cm. [1] (b) (iii) Values of d and D both with unit and d in range 4.0 ≤ d ≤ 6.0 cm. [1] (c) Six sets of readings of d and D scores 5 marks, five sets scores 4 marks etc. Incorrect trend then –1. Supervisor’s help –1. [5] Range of d: ∆d ≥ 40 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, for example d / m, d (m), 1/D (m–1). Consistency of presentation of raw readings: [1] All values of raw d and D must be given to the nearest mm. Significant figures: [1] Significant figures for 1/D must be the same as, or one more than, the number used in D. Calculation: (D – d)/D calculated correctly. [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 occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity which is being plotted. Scale markings must be no more than three large squares apart. Plotting of points: [1] All observations in the table must be plotted. Check that the points are correctly plotted. Work to an accuracy of half a small square in both x and y directions. 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 5) for this mark to be scored. Scatter of points must be less than ± 0.05 m–1 (0.0005 cm–1) of 1/D of a straight line. (ii) Line of best fit: [1] Judge by balance of all the 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. Allow one anomalous point only if clearly indicated (i.e. circled or labelled) by the candidate. GCE AS/A LEVEL – October/November 2011 9702 31 (iii) Gradient: [1] The hypotenuse of the triangle used must be at least half the length of the drawn line. Both read-offs must be accurate to half a small square in both x and y directions. The method of calculation must be correct. Intercept: [1] Either: Check correct read-off from a point on the line and substitution into y = mx + c. Read-off must be accurate to half a small square in both x and y directions. Allow ecf of gradient value. Or: Check the read-off of the intercept directly from the graph. (e) A = value of gradient, B = – (value of y-intercept). [1] A/B = k ± 5 cm with consistent unit. [1] [Total: 20]

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2 In this experiment you will investigate how the motion of a thin card shape depends on its size. You have been provided with two identical strips of card. Spare strips are available if necessary. (a) Measure and record the thickness t of one of the strips of card. t = ...........................................mm [1] (b) (i) Measure and record the length L of the same strip of card as shown in Fig. 2.1. w L Fig. 2.1 L = ................................................. [1] (ii) Estimate the percentage uncertainty in your value of L. percentage uncertainty = ................................................. [1] (c) (i) Measure and record the width w of the same strip as shown in Fig. 2.1. w = ...................................................... (ii) Determine the volume V of the strip, using the equation For Examiner’s V = t L w Use V = ................................................. [1] (d) (i) Use tape to stick the two strips together, so that they do not overlap, to make the shape shown in Fig. 2.2. L tape L L 2 2 Fig. 2.2 (ii) Use the pin to make a hole at the top of the vertical strip as shown in Fig. 2.3. For Examiner’s hole Use top of strip Fig. 2.3 The hole should be central and as near to the top as possible and be large enough for the card to swing freely on the pin. (iii) Using the cork and pin, suspend the card shape as shown in Fig. 2.4. pin stand bench Fig. 2.4

Mark scheme: 2 (a) Measurement of all raw values of t to nearest 0.01 mm or 0.001 mm and t in range 0.10 ≤ t ≤ 0.50 mm. [1] (b) (i) Value of L in range 26.0 cm ≤ L ≤ 30.0 cm with consistent unit to nearest mm. [1] (ii) Absolute uncertainty in L in range 1–2 mm (but if repeated readings have been taken then the absolute uncertainty could be half the range unless zero). Correct method shown to find the percentage uncertainty. [1] (c) (ii) Correct calculation of V with consistent unit. Allow ecf. [1] (e) Value of T in range 0.7 s ≤ T ≤ 1.5 s with consistent unit. Supervisor help –1. [1] Evidence of repeats. [1] (f) Second value of L in range 5 cm ≤ L ≤ 15 cm. [1] (g) Second value of T. [1] Quality: second value of T < first value of T. [1] (h) (i) Two values of k calculated correctly. [1] (ii) Justification of s.f. in k linked to raw data in L and T/t. [1] (iii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] GCE AS/A LEVEL – October/November 2011 9702 31 (i) (i) Limitations 4 max. (ii) Improvements 4 max. Do not credit A Two readings are not enough Take more readings and plot ‘Few readings’/‘take more (to draw a conclusion) a graph/calculate more k readings and calculate values (and compare) average k’/‘only one reading’ B Card does not swing freely/ Make hole bigger/bush or friction between pivot and bearing idea card C Difficult to judge end/start/a Use of fiducial marker/pointer Reaction time error/human complete swing reaction/difficult to know when to start/stop timer D Irregular/uneven/unusual Method of keeping shape swings/not in same vertical aligned vertically/turn off fans plane/centre of bottom rule not fixed E Oscillations die out quickly/ Use increased thickness of heavy damping card F T short/large uncertainty in T Improved method of timing Use of computer/light gates/ e.g. video and timer/frame-by- camera/high speed camera/ frame. Increase l/length of too fast/time too fast/time card more swings/time large no. of swings [Total: 20]

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