Cambridge A Level Physics 9702 — 2014 May/June Paper 3 · Variant 2

1 In this experiment, you will investigate the equilibrium of a rod supported by a spring. (a) The apparatus has been assembled for you as shown in Fig. 1.1. stand boss nail A plumb-line string boss spring nail B clamp string loop wooden rod bench Fig. 1.1 (i) Lift the end of the rod attached to the spring so that there is no tension in the spring. Measure and record the unstretched length l0 of the spring, as shown in Fig. 1.2. l 0 Fig. 1.2 l0 = ............................................ cm [1] (ii) Release the end of the rod. Suspend the mass M from the string loop. (b) (i) Move the string in the clamp to make the rod horizontal. (ii) Use the plumb-line to ensure that nail B is vertically below nail A, as shown in Fig. 1.3. nail A plumb-line h l nail B clamp holding mass M string bench Fig. 1.3 (iii) Measure and record the distance h between the two nails, and the length l of the spring, as shown in Fig. 1.3. h = ................................................. cm l = ................................................. cm [1] (c) Raise nail B and repeat (b) until you have six sets of values of h and l. 1 Include values for and (l – l0)2 in your table. h2 [10] 1 (d) (i) Plot a graph of (l – l0)2 on the y-axis against h2 on the x-axis. [3] (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 l and h are related by the equation p (l – l0)2 = + q h2 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] Please turn over for Question 2. You may not need to use all of the materials provided.

Mark scheme: 1 (a) (i) Value of l 0 in range 4.0 cm Y l 0 Y 8.0 cm. [1] (b) (iii) Value of h to nearest mm, in the range 40.0 cm Y h Y 50.0 cm. [1] (c) Six sets of values for h and l scores 5 marks, five sets scores 4 marks, etc. [5] Incorrect trend –1. Help from Supervisor –1. Range: [1] h values must include 20 cm or less. 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. 1/h2/cm–2 or 1/h2 (1/cm2) but not 1/h2(cm2). Consistency: [1] All values of h and l must be given to the nearest mm only. Significant figures: [1] Every value of 1/h2 must be given to the same s.f. as (or one greater than) the s.f. in the corresponding h. Calculation: [1] Values of (l –l 0)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 3 large squares apart. Plotting: [1] All observations in the table must be plotted. Diameter of plotted points must be Y half a small square (no “blobs”). Work to an accuracy of half a small square. Quality: [1] All points must be plotted (at least 5) for this mark to be scored. Scatter of points must be within ±10 cm2 of (l –l 0)2 from a straight line. (ii) Line of best fit: [1] Judge by balance of all points 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 plot 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 A LEVEL – May/June 2014 9702 32 (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: Read-off from a point on the line is substituted into y = mx + c. Read-off must be accurate to half a small square in both x and y directions. Or: Check read-off of the intercept directly from the graph. (e) p = value of the gradient, and q = value of the intercept. [1] Dimensionally correct units for p and q. [1] [Total: 20]

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2 In this experiment, you will investigate the motion of a mass and a spring. (a) You are provided with a spring. (i) Measure and record the diameter d of the coiled section of the spring as shown in Fig. 2.1. Record the number n of turns in the coiled section. d Fig. 2.1 d = ................................................. cm n = ...................................................... [1] (ii) Calculate the length l of wire used to make the coiled section of the spring using the relationship l = πnd. l = ............................................ cm [1] (b) (i) Set up the apparatus as shown in Fig. 2.2 with mass 1 suspended from the spring and secured with Blu-Tack. boss bolt stand spring Blu-Tack mass one vertical oscillation bench Fig. 2.2 (ii) Pull the mass down approximately 2 cm and release it. One vertical oscillation is shown in Fig. 2.2. Measure and record the time t for the mass to make 10 vertical oscillations. t = ..................................................[2] (c) (i) Lower the bolt until the bottom of the stationary mass is approximately 6 cm above the bench, as shown in Fig. 2.3. bolt mass 6 cm (approximately) bench Fig. 2.3 (ii) Pull the mass down until it touches the bench. Release the mass and watch the loop on the bolt, looking to see if the loop rises above the bolt producing a gap as shown in Fig. 2.4. gap between loop and bolt bolt loop Fig. 2.4 (iii) Keep raising the bolt and repeating (ii) until the loop just rises above the bolt at the top of the first oscillation. With the mass stationary, measure and record the distance A from the bottom of the mass to the bench. A = ..................................................[1] (d) Estimate the percentage uncertainty in your value of A. percentage uncertainty = ..................................................[1] (e) Detach the mass from the spring. Repeat (b) and (c) using mass 2. t = ...................................................... A = ...................................................... [2] (f) It is suggested that the relationship between A, t and l is A = kt 2l where k is a constant. (i) Using your data, calculate two values of k. first value of k = ...................................................... second value of k = ...................................................... [2]

Mark scheme: 2 (a) (i) Value for d to nearest mm, in range 1.0 cm Y d Y 2.0 cm. [1] (ii) Correct calculation of l. [1] (b) (ii) Value for t in range 4.0s Y t Y 10.0 s, with unit. [1] Evidence of repeat readings of t. [1] (c) (iii) Value for A to nearest mm, with unit. [1] (d) Absolute uncertainty in A in range 2 to 5 mm. [1] If repeated readings have been taken, then absolute uncertainty could be half the range (but not zero) only if working shown. Correct method of calculation to obtain percentage uncertainty. (e) Second value of t. [1] Second value of A. [1] (f) (i) Two values of k calculated correctly. [1] kl in range 0.20 to 0.30 cm s–2. [1] (ii) Justification based on the number of s.f. in d, n, t and A (not just “raw readings”). [1] (iii) Valid comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] GCE A LEVEL – May/June 2014 9702 32 (g) (i) Limitations (4 max) (ii) Improvements (4 max) Do not credit A Two readings are not Take more readings (for Not enough repeat readings enough to draw a valid different masses) and plot a Few readings conclusion graph, or take more readings Idea of repeats and compare k values “Too few readings/two readings” on its own B Difficult to measure d, with Use vernier calipers/micrometer “Parallax error” on its own reason, e.g. parallax error/ Measure inside and outside “Calipers” on its own measuring outside diameter and find average diameter/loop gets in the way C Difficult to judge exactly Video + timer/video and view Human/reaction time error when 10 oscillations frame-by-frame. completed Use distance sensor in stated High speed cameras/slow and correct position motion cameras Use a (fiducial) marker at centre of oscillation/equilibrium position Oscillations too fast Light gate at equilibrium position/centre of oscillation D Mass swings as it Use tube to act as a guide oscillates/non-uniform Use deeper groove on bolt oscillation/spring moves Fix top of spring to bolt with, along bolt e.g. Blu-tack/Sellotape E Difficult to judge when Use pressure sensor on bolt “Video + slow motion” on its contact is lost/hard to see Use video close-up/zoom lens/ own gap magnifying glass Video + slow-motion, linked to observing gap Better/more sensitive method of adjusting height of bolt, e.g. lab jack F n is not a whole number Measure n to nearest ¼ turn Do not credit use of an assistant, fans, air conditioning, or use of computers/data loggers on its own. [Total: 20]

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