Cambridge A Level Physics 9702 — 2014 May/June Paper 3 · Variant 1

1 In this experiment, you will investigate a system in equilibrium due to several forces. (a) Measure and record the distance L0 between the ends of the spring, as shown in Fig. 1.1. Note that this distance includes the two loops at the ends. L0 loop Fig. 1.1 L0 = ..............................................m [1] (b) (i) Set up the apparatus as shown in Fig. 1.2. Mass m should be 0.200 kg. Do not change the height of the pulley or the clamp. rod of pulley clamp L θ spring knot mass m string stand mass X bench Fig. 1.2 (ii) Adjust the apparatus until the angle θ is 90°. You may move the stands sideways or slide the knot along the string. (iii) Measure and record the distance L between the ends of the spring loops. L = ..............................................m [1] (iv) Calculate the extension e of the spring using e = L – L0. e = ...................................................m (c) Vary m and repeat (b)(ii), (b)(iii) and (b)(iv) until you have six sets of readings of m and L. Include values of m 2, e and e 2 in your table. [10] (d) (i) Plot a graph of e 2 on the y-axis against m 2 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 e and m are related by the equation e 2 = – P m 2 + Q where P and Q are constants. Use your answers in (d)(iii) to determine the values of P and Q. Give appropriate units. P = ...................................................... Q = ...................................................... [1] (f) The mass M of X is given by Q M = . P Use your answers in (e) to determine the value of M. Include a unit for M. M = ..................................................[1] You may not need to use all of the materials provided.

Mark scheme: 1 (a) Value of L0 in range 0.045 m–0.070 m (4.5 to 7.0 cm). [1] If out of range, compare to Supervisor’s value ± 20%. (b) (iii) Value of L > L0. [1] (c) Six sets of readings of m and L scores 5 marks, five sets scores 4 marks, etc. [5] Incorrect trend then –1. Correct trend is L decreases as m increases for all m values. Major help from Supervisor –2. Minor help from Supervisor –1. Range: at least one value of m less than 200 g and one value more than 200 g. [1] 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. θ / o, L / m, m2 / kg2, e / m, e2(m2). Consistency: [1] All values of L must be given to the nearest mm only. Significant figures: Significant figures for every row of m2 same as (or one greater than) the s.f. in m as recorded in table. [1] Calculation: [1] Values of e2 calculated correctly to the number of significant figures given by the candidate. (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 plots must be Y half a small square (no “blobs”). Work 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 less than ± 0.0005 m2 of e2 from a straight line. (ii) Line of best fit: [1] Judge by balance of all points on the grid about the candidates’ 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 – May/June 2014 9702 31 (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 the x and y directions. The method of calculation must be correct. y-intercept: [1] Either: Check 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: Check read-off of the intercept directly from the graph. (e) P = – value of the gradient and Q = value of the y-intercept. [1] Do not allow fractions. Do not allow substitution methods. (f) Check substitution and value of M in range 0.100–0.500 kg with unit. [1] [Total: 20]

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2 In this experiment, you will investigate the motion of a hacksaw blade supported by a G-clamp. (a) Using the Blu-Tack, attach the two slotted masses as close as possible to one end of the hacksaw blade, as shown in Fig. 2.1. Blu-tack hacksaw blade mass mass Fig. 2.1 (b) (i) Set up the apparatus as shown in Fig. 2.2. masses hacksaw blade x jaw of G-clamp bench Fig. 2.2 (ii) Measure and record the distance x between the top of the jaw of the G-clamp and the centre of the masses, as shown in Fig. 2.2. x = .................................................[2] (iii) Estimate the percentage uncertainty in your value of x. percentage uncertainty = ..................................................[1] (c) (i) Gently displace the top end of the hacksaw blade to the left. Release the blade and watch the movement. The blade will move to the right and back towards the left, completing a swing as shown in Fig. 2.3. one complete swing bench Fig. 2.3 (ii) The time taken for one complete swing is T. By timing several of these complete swings, determine an accurate value for T. T = ..................................................[2] 1 (iii) Calculate the frequency f of the swings where f = . T f = .............................................Hz [1]

Mark scheme: 2 (b) (ii) Value of x in the range 25.0–35.0 cm with unit. [1] x to the nearest mm [1] (iii) Absolute uncertainty in x in range 2 mm–5 mm. [1] If repeated readings have been taken, then the uncertainty can be half the range (not zero) only if working shown. Correct method of calculation to obtain percentage uncertainty. (c) (ii) Value of T with unit. [1] Evidence of repeats. [1] (iii) Correct calculation of f. [1] (d) (ii) Second value of x. [1] Second value of T. [1] Second value of T < first value of T. [1] (e) (i) Two values of k calculated correctly. [1] (ii) Justification of significant figures in k linked to significant figures in x and T / time. (Do not allow “raw readings”.) [1] (iii) Valid comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] GCE AS/A LEVEL – May/June 2014 9702 31 (f) (i) Limitations (4 max) (ii) Improvements (4 max) Do not credit A Two readings not enough to Take more readings for Not enough repeat draw a conclusion. different lengths and plot a readings. graph or take more readings Few readings. and compare k values. Idea of repeats. “Too few readings / two readings” on its own. B Difficulty linked to timing with Improved method of timing, “Human errors / reaction reason, e.g. time small / short / e.g. video with timer / video and time” on their own. vibrates fast / high frequency / view frame by frame / light gate “Light gate” on its own. oscillates fast / swings fast. placed at the centre / motion Moves fast. or sensor at side of blade (to Video and playback. Large uncertainty in time with timer / datalogger display). Fans. reason. Longer blade. or Simultaneous release of Human reaction time with blade and start timer. reason, e.g. short time. Amplitude. High speed camera or slow motion cameras. C Unevenness of oscillation or Improved method of smoother G-clamp moving. oscillation, e.g. use of wooden block either side of hacksaw blade. Method of fixing G-clamp, e.g. clamp G-clamp (to table). D Difficulty judging centre of Use masses without slots / Blu Tack. masses (due to slots). measure to the top and bottom Masses different heights. and average. E Difficult to measure x with Improved method to measure Uncertainty in metre rule. reason, e.g. difficult to know x, e.g. description of use of set Parallax error. where to start x as jaws of square clamp are rounded / blade may not be vertical (due to clamp). F Small range for x for measurable times [Total: 20]

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