Cambridge A Level Physics 9702 — 2015 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate forces in equilibrium. (a) Assemble the apparatus as shown in Fig. 1.1. The angle θ should be approximately 150°. String AB should be parallel to the bench, and the bottom of mass M should be approximately 10 cm above the bench. boss L string spring nail A B e stand stand M § 10 cm mass EHQFK Fig. 1.1 (b) (i) Measure and record the angle θ between the string attached to mass M and the string attached to the spring, as shown in Fig. 1.1. θ = ...............................................° [1] (ii) Measure and record the length L of the coiled part of the spring, as shown in Fig. 1.1. L = ................................................. [1] (c) (i) Change the distance between the stands. Adjust the height of A until string AB is parallel to the bench. If the apparatus is unstable, you may need to use the G-clamp to secure one of the stands to the bench. (ii) Measure and record θ and L. θ = .....................................................° L = ...................................................... (d) Repeat (c) until you have six sets of values of θ and L. Include your values from (b) and (c). 1 Also include values of in your table. sin (θ –90°) [10] 1 (e) (i) Plot a graph of on the y-axis against L on the x-axis. [3] sin (θ –90°) (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] (f) The quantities θ and L are related by the equation 1 = a L + b sin (θ –90°) where a and b are constants. Using your answers in (e)(iii), determine the values of a and b. Give appropriate units. a = ...................................................... b = ...................................................... [2] You may not need to use all of the materials provided.

Mark scheme: 1 (b) (i) Value of θ to the nearest degree and in the range 135° to 165°. [1] (ii) Value of L in range 5.0 to 10.0 cm, with unit. [1] (d) Six sets of readings of θ and L scores 5 marks, five sets scores 4 marks etc. [5] Incorrect trend –1. Help from Supervisor –1. Range: [1] θmax ⩾ 160° and θmin ⩽ 140°. 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. θ / °. 1/sin(θ – 90°) must have no unit. Consistency: [1] All values of L must be given to the nearest mm. Significant figures: [1] Every value of 1/sin(θ – 90°) must be given to 2 or 3 significant figures only. Calculation: [1] Values of 1/sin(θ – 90°) calculated correctly to the number of significant figures given by the candidate. (e) (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 that is being plotted. Scale markings should be no more than three large squares apart. Plotting: [1] All observations in the table must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square (no “blobs”). Points must be plotted 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 no more than ±0.3 (to scale) cm in the L direction 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. Lines must not be kinked or thicker than half a square. (iii) Gradient: [1] The hypotenuse of the triangle must be greater than half the length of the drawn line. Do not allow ∆x / ∆y. Sign of gradient must match graph drawn. Both read-offs must be accurate to half a small square in both the x and y directions. y-intercept: [1] Either: Correct read-offs from a point on the line substituted into y = mx + c or an equivalent expression. Read-offs must be accurate to half a small square in both x and y directions. Or: Intercept read directly from the graph, with read-off accurate to half a small square. (f) Value of a = candidate’s gradient and value of b = candidate’s intercept. [1] Unit for a is correct (e.g. cm–1) and no unit for b. [1]

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2 In this experiment, you will investigate the relationship between the performance of an electrical component and its volume. (a) You are provided with two cylindrical components. (i) Measure and record the diameter d and the length l of the larger cylindrical component, as shown in Fig. 2.1. d + l Fig. 2.1 d = ...................................................... l = ...................................................... [2] π d 2 l (ii) Calculate the volume V of the component using V = . 4 V = ................................................. [1] (b) Justify the number of significant figures you have given for your value of V. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ..................................................................................................................................... [1] (c) (i) Assemble the circuit shown in Fig. 2.2, using the larger cylindrical component. Ensure that the positive terminals are all connected as shown. Switch on the power supply. power supply + – S + cylindrical component + Fig. 2.2 (ii) Close switch S and watch the LED light up. Open switch S and watch the LED gradually go out. (iii) Take measurements to find the time t between opening the switch S and the LED going out. t = ................................................. [2] (d) Estimate the percentage uncertainty in your value of t. percentage uncertainty = ................................................ [1] (e) Using the smaller cylindrical component, repeat (a) and (c). d = ...................................................... l = ...................................................... V = ...................................................... t = ...................................................... [3] (f) It is suggested that the relationship between t and V is t = k V where k is a constant. (i) Using your data, calculate two values of k. first value of k = ...................................................... second value of k = ...................................................... [1]

Mark scheme: 2 (a) (i) All values of d to nearest mm, with unit, in range 5 to 30 mm. [1] Value of l greater than value of d. [1] (ii) Correct calculation of V with consistent unit. [1] (b) Justification for significant figures in V linked to significant figures in d and l. [1] (c) (iii) t in range 5.00 s to 30.00 s, with unit. [1] Evidence of repeat readings of t. [1] (d) Absolute uncertainty in t in range 0.5 s to 5.0 s and correct method of calculation to obtain percentage uncertainty. If repeated readings have been taken, then the absolute uncertainty can be half the range (but not zero) if working is clearly shown. [1] (e) Second values of d and l. [1] Second value of t. [1] Second value of t < first value of t. [1] (f) (i) Two values of k calculated correctly. [1] (ii) Valid comment consistent with the calculated values of k, testing against a criterion specified by the candidate. [1] (g) (i) Limitations (4 max.) (ii) Improvements (4 max.) Do not credit A Not enough readings to draw a Take more readings and plot a Few readings/ conclusion graph/ only one reading/ obtain more k values and not enough readings compare for an accurate result/ “repeat readings” on its own/ take more readings and (calculate) average k B d is small/large uncertainty in d Improved method of measuring Difficult to measure d/ d e.g. micrometer/vernier parallax error/ calipers/digital calipers/travelling “calipers” on its own/ microscope use bigger/larger components C Volume of component not accurate, Method to find volume of with reason e.g. component not component e.g. use liquid cylindrical/has groove. displacement method D Difficult to judge/know/see when Use dark(ened) room/ Use video LED goes out. light meter/ light sensor/ cardboard tube over LED/ voltmeter to measure time for p.d. to fall below specific value E Poor/dirty/loose contacts Method of cleaning contacts e.g. iron wool

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