Cambridge A Level Physics 9702 — 2013 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate how the forces supporting a wooden strip change as the position of a suspended mass is moved. (a) (i) Suspend the single spring and the mass hanger from the rod of one of the clamps. Measure and record the height h1 of the mass hanger above the bench, as shown in Fig. 1.1. rod of clamp spring 50 g mass hanger h1 bench Fig. 1.1 h1 = ...................................................... (ii) Add the 50 g slotted mass to the hanger. Measure and record the new height h2 of the mass hanger above the bench. h2 = ...................................................... [1] (iii) Calculate the change in height C, where C = h1 – h2. C = ...................................................... (b) (i) Assemble the apparatus as shown in Fig. 1.2, with the mass M near to the middle For of the wooden strip. Examiner’s Use spring LA LB wooden strip spring x string loop M 50 g mass hanger and 50 g slotted mass bench Fig. 1.2 (ii) Adjust the apparatus so that the wooden strip is horizontal and the springs are vertical. (iii) Measure and record the distance x from the left-hand hole in the wooden strip to the string loop supporting M, as shown in Fig. 1.2. x = ...................................................... (iv) Measure and record the length LA of the coiled section of the left-hand spring, and the length LB of the coiled section of the right-hand spring. LA = ...................................................... LB = ...................................................... [1] (c) Reposition the string loop supporting M. For Examiner’s Repeat (b)(ii), (b)(iii) and (b)(iv) until you have six sets of values of x, LA and LB. Use Include values for – and for (LA – LB) in your table. (LA LB) C [10] (d) (i) Plot a graph of (LA – LB) on the y-axis against x on the x-axis. [3] C (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 LA, LB, C and x are related by the equation For Examiner’s Use (LA – LB) = a x + b C where a and b are constants. Use your answers from (d)(iii) to determine the values of a and b. Give appropriate units. a = ....................................................... b = ....................................................... [2] You may not need to use all of the materials provided. For Examiner’s Use

Mark scheme: 1 (a) (ii) Value of h2<h1, with consistent unit. [1] (b) (iv) First values of LA and LB, with unit, and value of LA – LB in range 1.0 to 6.0 cm. [1] (c) Six sets of values for x, LA and LB scores 5 marks, five sets scores 4 marks etc. [5] Incorrect trend –1. Help from Supervisor –1. Range: x values must include 20.0 cm or less and 80.0 cm or more. [1] Column headings: [1] Each column heading must contain a quantity and a unit where appropriate. The unit must conform to accepted scientific convention, e.g. x/cm or x (cm). Consistency of presentation of raw readings: [1] All values of x must be given to the nearest mm. Significant figures: [1] Every value of (LA–LB)/C must be given to the same s.f. as (or one more than) the least s.f. in C or in (LA–LB). Calculation: (LA–LB)/C calculated correctly. [1] (d) (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 must be plotted. Diameter of plotted points must be ≤ half a small square (no “blobs”). Plots must be accurate to half a small square. Quality: [1] All points in the table must be plotted for this mark to be scored. All points must be within ± 4 scale cm, on the x–axis, of 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 by the candidate. Line must not be kinked or thicker than half a small square. GCE AS/A LEVEL – October/November 2013 9702 34 (iii) Gradient: [1] The hypotenuse 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. 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. (e) Value of a = candidate’s gradient and value of b = candidate’s intercept. [1] A value presented as a fraction is not allowed. Correct units for a (e.g. cm–1) and b (no unit), and gradient in range –0.050 to –0.150 cm–1 (–5.0 to –15.0 m–1). [1] [Total: 20]

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2 In this experiment, you will investigate the equilibrium of a spool of thread. (a) (i) Using the smaller of the two spools provided, take measurements to determine the outside diameter D and the inner diameter d, as shown in Fig. 2.1. spool D d thread Fig. 2.1 D = ................................................mm d = ................................................mm [2] d (ii) Calculate the ratio R, where R = D. R = ..................................................[1] (b) Justify the number of significant figures that you have given for your value of R. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[1] (c) Use the stand, boss and clamp to support the protractor as shown in Fig. 2.2. For Examiner’s Use protractor clamp boss stand bench Fig. 2.2 (d) (i) Using the smaller of the two spools, wrap the thread around its inner diameter until there is about 30 cm of thread left unwound. (ii) With the spool on the bench, gently pull the thread vertically as shown in Fig. 2.3. direction of movement of end of thread thread spool bench Fig. 2.3 (iii) The spool will move to the left until the thread reaches a constant angle θ to the For vertical with the spool rotating but not moving along the bench, as shown in Fig. 2.4. Examiner’s Use direction of pull thread e rotating spool bench Fig. 2.4 (iv) Measure and record the angle θ. θ = ..................................................[2] (e) Estimate the percentage uncertainty in your value of θ. percentage uncertainty = ..................................................[1]

Mark scheme: 2 (a) (i) Raw value(s) for d to nearest 0.1 mm or nearest 0.01 mm. [1] d in range 10.0 to 15.0 mm. [1] (ii) Correct calculation of R. [1] (b) Valid justification for s.f. in R based on s.f. in d and D. [1] (d) (iv) θ in range 10o to 50o, with unit. Raw reading(s) must be integer value(s). [1] Evidence of repeated readings of θ. [1] (e) Estimate of percentage uncertainty based on an absolute uncertainty of 2o to 10o [1] (or half the range provided this is not zero), and correct method of calculation. (f) Second values for d and D. [1] Second value of θ. [1] Quality: Second θ less than first θ. [1] (g) (i) Correct calculation of two values of k. [1] (ii) Sensible comment relating to the calculated values of k, testing against a [1] criterion specified by the candidate. GCE AS/A LEVEL – October/November 2013 9702 34 (h) (i) Limitations (4 max) (ii) Improvements (4 max) Do not credit A Two readings are not enough Take many R values and plot ‘few readings’/ ‘take more (to draw a valid conclusion) a graph/ calculate more k readings and calculate values and compare average’/‘only one reading’ B Spool does not roll straight/ Roll spool between guides/ Lubricate bench or spool spool topples over/ use wider spool jerky motion C Difficult to judge θ as it varies, equilibrium position not maintained D Difficult to measure θ due to Method to reduce parallax parallax (e.g. shadow method) E Difficult to pull thread when Specified thread guiding measuring θ / method (e.g. pulley or rod) difficult to watch spool and protractor at same time F Difficult to align thread with Take photo or video and centre of protractor measure θ on image (e.g. photo or screen) G Difficult to make protractor Use plumb-line/detail of vertical another sensible method (e.g. use set square on bench) Do not allow ‘repeated readings’ Do not allow ‘use a computer to improve the experiment’ [Total: 20]

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