Cambridge A Level Physics 9702 — 2014 May/June Paper 3 · Variant 4

1 In this experiment, you will investigate the motion of a system of masses as its shape is changed. (a) You are provided with a length of wire, bent into two arms, with a mass attached at the end of each arm as shown in Fig. 1.1. i wire tape mass Fig. 1.1 (i) Measure and record the angle i between the two arms. i = .................................................. [1] 2 i (ii) Calculate sin , where c 2 m 2 i i i sin = sin # sin . c 2 m c 2 m c 2 m 2 i sin = ....................................................... c 2 m (b) You are provided with a spring suspended from a stand. A hook is suspended from the bottom of the spring. Hang the wire from the upper part of the hook and hang the mass hanger from the lower part of the hook as shown in Fig. 1.2. clamp spring hook wire mass hanger stand bench Fig. 1.2 (i) Twist the mass hanger through about 45° and release it so that the mass hanger and wire rotate back and forth as shown in Fig. 1.3. wire one complete swing mass hanger Fig. 1.3 (top view) (ii) Measure and record the time t for the mass hanger and wire to make 5 complete swings. t = .................................................. [2] (c) Remove the wire from its hook. Bend the wire to change the angle q. The arms of the wire must remain straight. Repeat (a) and (b) until you have five sets of readings for q and t. 2 2 i Include values for t and sin in your table. c 2 m [9] 2 2 i(d) (i) Plot a graph of t on the y-axis against sin on the x-axis. [3] c 2 m (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ....................................................... y-intercept = ....................................................... [2] (e) The quantities t and q are related by the equation 2 2 i t = p + q sin c 2 m where p and q are constants. Using your answers from (d)(iii), determine the values of p and q. Give appropriate units. p = ....................................................... q = ....................................................... [2] You may not need to use all of the materials provided.

Mark scheme: 1 (a) (i) Value for θ in range 80° to 100°, with unit. [1] (b) (ii) Value for t in range 10 to 40 s, with unit.. [1] Evidence of repeat readings of t. [1] (c) Five sets of values for θ and t scores 4 marks, four sets scores 3 marks etc. [4] Incorrect trend –1. Help from Supervisor –1. Range: [1] θ values must include 75° or less and 105° or more. Column headings: [1] Each column heading must contain a quantity and an appropriate unit. The presentation of quantity and unit must conform to accepted scientific convention e.g. t2 / s2 or t2 (s2), θ (°) or θ (deg) etc. sin2(θ / 2) must have no unit. Consistency: [1] All values of t must be given to the nearest 0.1 s, or all to the nearest 0.01 s. Significant figures: [1] Every value of t2 must be given to the same s.f. as (or one greater than) the s.f. in the corresponding t. Calculation: [1] Values of sin2(θ / 2) calculated correctly. (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 must 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”). Plotting must be accurate to 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 within ± 20 s2 of a straight line in the y (t2) direction. GCE AS/A LEVEL – May/June 2014 9702 34 (ii) Line of best fit: [1] Judge by balance of all points on the grid about the candidate's line (at least 4 points). There must be an even distribution of points either side of the line along the full length. Allow one anomalous plot only if clearly indicated by the candidate. Line must not be kinked or thicker than half a small square. (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 x and y directions. y-intercept: [1] Either: Correct read-off from a point on the line 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) q = candidate's gradient and p = candidate's intercept. [1] Correct units for q and p (s2 for q and s2 for p). [1] [Total: 20] GCE AS/A LEVEL – May/June 2014 9702 34

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2 In this experiment, you will investigate the collision between two spheres. (a) You are provided with two spheres. Take measurements to find the average radius r of the spheres. r = .......................................... mm [1] (b) You are provided with a flat board, as shown in Fig. 2.1. wooden strip sticky surface l small hole board B A centre line e Fig. 2.1 A wooden strip with a sticky surface is attached to the board, and there is a small hole in the board. (i) Measure and record the distance l between the small hole and the sticky surface. l = .......................................... mm [1] (ii) Measure and record the perpendicular distance e between the centre line and the line labelled A. e = .......................................... mm [1] (c) (i) You are provided with a ramp with a groove in it. Position the ramp on the board with the centre of the groove along line A, and position one of the spheres in the hole, as shown in Fig. 2.2. ramp sphere positioned in hole centre of groove aligned with line A B A Fig. 2.2 (ii) Place the second sphere on the groove and release it so that it rolls down and hits the sphere in the hole. Both spheres will roll forward and hit the wooden strip. Measure and record the distance x between the centre of the right-hand sphere and the centre line, as shown in Fig. 2.3. x position of sphere hitting the wooden strip B A Fig. 2.3 x = .......................................... mm [2] (iii) Estimate the percentage uncertainty in your value of x. percentage uncertainty = .................................................. [1] (iv) Before the sphere hits the wooden strip, its path makes an angle i with the centre line. Calculate i using the relationship x tan i = ` j. l – r i = ................................................. [2] (d) Repeat (b)(ii), (c)(i), (c)(ii) and (c)(iv) with the distance e measured to line B and the centre of the groove along line B. e = ................................................ mm x = ................................................ mm i = ...................................................... [1]

Mark scheme: 2 (a) r in range 5.0 mm to 12.0 mm and to nearest 0.1 mm or better. [1] (b) (i) Value for l in range 61.0 mm to 65.0 mm. [1] (ii) Value for e in range 6.0 mm to 8.0 mm. [1] (c) (ii) Value for x. [1] Evidence of repeat readings of x. [1] (iii) Absolute uncertainty in x in range 2 to 9 mm. [1] If repeated readings have been taken, then absolute uncertainty could be half the range (but not zero) only if working is shown. Correct method of calculation to obtain percentage uncertainty. (iv) Calculated value of θ correct. [1] θ given to 2 or 3 significant figures. [1] (d) Second values of e and x. [1] (e) (i) Two values of k calculated correctly. [1] Both values for k in range 0.80 to 1.20. [1] (ii) Valid comment consistent with the calculated values of k, testing against a criterion specified by the candidate. [1] GCE AS/A LEVEL – May/June 2014 9702 34 (f) Limitations (4 max) Improvements (4 max) Do not credit A Two readings are not enough Take more readings and Repeat readings / to draw a valid conclusion plot graph / too few readings / take more readings and two readings compare k values B Difficult to align groove with Mark centre line of groove / line / method of aligning groove difficult to estimate centre of (e.g. use lines on groove paper / use graph paper / transparent ramp) C e is small so uncertainty in e Use larger spheres to Just “use larger is large / enable larger e spheres” small change in e gives large change in θ D Parallax error when Use set square (with detail measuring x of workable method) E Difficult to locate centre of Measure to edge of sphere Difficult to locate sphere when measuring x and add r centre of sphere when measuring r F Sphere rolls slightly after Use video with scale (in High speed hitting tape / view) / camera / sphere does not stick Description of workable slow motion improvement (e.g. powder camera / on strip / plasticine surface) video camera / stickier surface / magnets [Total: 20]

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