Cambridge A Level Physics 9702 — 2014 May/June Paper 3 · Variant 5

1 In this experiment, you will investigate a system in equilibrium due to several forces. (a) You have been provided with a wooden beam with 11 holes. Measure and record the distance k along the wooden beam between the centres of hole 1 and hole 5 as shown in Fig. 1.1. k wooden beam string spring Fig. 1.1 k = ..................................................... (b) (i) Set up the apparatus as shown in Fig. 1.2 with the nail through hole 6 of the wooden beam. boss rod of clamp stand spring 15 cm nail boss hole 1 hole 6 wooden beam string stand mass m bench Fig. 1.2 The mass m is 300 g. Position the mass m approximately 15 cm from hole 1. (ii) Adjust the apparatus so that the spring is vertical and the wooden beam is horizontal. The distance a is the distance between the nail and the string attached to the spring. The distance b is the distance between the nail and the string attached to the mass as shown in Fig. 1.3. a b bench Fig. 1.3 (iii) Measure and record a and b. a = ..................................................... b = ..................................................... [1] (iv) Measure and record the length L of the stretched spring as shown in Fig. 1.4. spring L string supporting wooden beam Fig. 1.4 L = ................................................. [1] (c) Vary a by moving the nail to a different hole. Adjust b until the value of L is the same as in (b)(iv). Ensure that the spring is vertical and the beam is horizontal. Measure and record a and b. a = ..................................................... b = ..................................................... (d) Repeat (c) until you have six sets of readings of a and b. 1 a Include values of and in your table. b b [10] 1 a(e) (i) Plot a graph of on the y-axis against on the x-axis. [3] b b (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 a and b are related by the equation 1 P a = – + Q b b where P and Q are constants. Use your answers in (e)(iii) to determine the values of P and Q. Give appropriate units. P = ..................................................... Q = ..................................................... [1] (g) The mass M of the wooden beam is given by m M = . kQ Use values in (a), (b)(i) and (f) 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 (b) (iii) Values of a in range 53.0 cm – 57.0 cm and b < a with unit. [1] (iv) Value of L in the range 12.0 cm – 16.0 cm with unit. [1] (d) Six sets of readings of a and b scores 5 marks, five sets scores 4 marks, etc. [5] Incorrect trend –1 (correct trend is b increases as a increases). Help from Supervisor –1. Range: ∆a [ 39 cm. [1] Column headings: [1] Each column heading must contain a quantity and unit. The presentation of quantity and unit must conform to accepted scientific convention, e.g. (1 / b) / m–1. Consistency: [1] All values of a and b must be given to the nearest mm. Significant figures: [1] Significant figures for every row of values of 1 / b same as (or one greater than) b as recorded in table. Calculation: [1] Values of a / b calculated correctly. (e) (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 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 ± 0.001 cm–1 (0.1 m–1) of 1 / b 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 by the candidate. Line must not be kinked or thicker than half a small square. GCE AS/A LEVEL – May/June 2014 9702 35 (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. (f) Value of P = –gradient and value of Q = intercept. [1] (g) Value of M in range 40–200 g with unit. No POT error allowed. [1] [Total: 20]

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2 In this experiment, you will investigate how the extension of a Plasticine cylinder under an applied load depends on the diameter of the cylinder. (a) (i) Use the boards to roll the Plasticine into a cylinder of uniform diameter and approximate length 20 cm as shown in Fig. 2.1. d 20 cm Fig. 2.1 (ii) Use the micrometer to measure the diameter d of the cylinder as shown in Fig. 2.1. Record d. d = ................................................. [3] (iii) Estimate the percentage uncertainty in your value of d. percentage uncertainty = ................................................. [1] (b) (i) Make two shallow marks on the Plasticine cylinder as shown in Fig. 2.2. The distance x between the marks should be approximately 10 cm. x Fig. 2.2 The marks should not be deep enough to affect the strength of the cylinder. (ii) Measure and record x. x = ..................................................... (c) (i) Attach the clip to one end of the cylinder. Hold the other end of the cylinder so that it hangs vertically as shown in Fig. 2.3. cylinder clip Fig. 2.3 (ii) Suspend a mass of 400 g from the clip as shown in Fig. 2.4 for a time of 60 s. If the cylinder breaks within this time, repeat (a), (b) and (c)(i) and suspend a mass of 300 g for 60 s. If necessary, cross out your answers and write in your new answers. You will not be penalised for this. cylinder clip handle 400 g mass Fig. 2.4 (iii) Carefully remove the mass and clip from the cylinder. (iv) Measure and record the distance x1 between the two marks on the cylinder. x1 = ................................................. [1] (v) Calculate the extension e of the cylinder between the marks using e = x1 – x. e = ................................................. [1]

Mark scheme: 2 (a) (ii) Values of d to the nearest 0.01 mm with unit. [1] 6.00 mm Y d Y 10.00 mm. If out of range allow Supervisor’s value ± 2.00 mm. [1] Evidence of repeat readings. [1] (iii) Absolute uncertainty in d in range 0.05 mm–2.00 mm. [1] If repeated readings have been taken, then the uncertainty could be half the range (but not zero) only if the working is shown. Correct method of calculation to get percentage uncertainty. (c) (iv) Value of x1 > x with unit to the nearest mm. [1] (v) Correct calculation of e. [1] (d) (ii) Second value of d. [1] Second value of x1. [1] Second value of e < first value of e. [1] (e) (i) Two values of k calculated correctly. [1] (ii) Justification based on the number of significant figures in e (or x1 – x) and d. [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 35 (f) (i) Limitations (4 max) (ii) Improvements (4 max) Do not credit A Two readings not enough to draw a Take many readings for different Repeat readings conclusion diameters and plot a graph Few readings Too few readings / only two readings B Large uncertainty in extension Use longer / thinner cylinders or because extension small thinner central portion / time for hanging longer / greater mass to give greater extension C Difficult to roll uniform cylinder / Viable suggestion for cylinder not symmetrical / not improvement, e.g. spacers, uniform diameter / density or mould, force through hole consistency not the same D Reading of x1 is imprecise because Improved method of marking marks have widened without a dent E Difficulty with clamping the Improved method to attach plasticine, e.g. breaks prematurely / weight to plasticine, twists in clamp e.g string loop through handles / place clamp lengthways F Micrometer digs into plasticine and Improved method to measure d, may weaken it / gives incorrect e.g. travelling microscope / work diameter reading out diameter from volume or circumference G Difficulties relating to the properties Use new piece of plasticine of the plasticine over time, e.g. high each time / roll and leave until temperature making too reaches room temperature soft / picking up impurities / re- breaking at fractured points / as roll temperature increases and affects [Total: 20]

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