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

1 In this experiment, you will investigate the equilibrium of a wooden rod. (a) Set up the apparatus as shown in Fig. 1.1. KRRN VWDQG VWULQJ / PDVV P VSULQJ K ZRRGHQ URG e EHQFK Fig. 1.1 The mass m should be 60 g. The string should be approximately half-way along the wooden rod. The spring should be horizontal. (b) (i) Measure and record the length L of the coiled part of the spring. L = ................................................. [1] (ii) Measure and record the height h of the loop of the spring above the bench. h = ..................................................... (iii) Measure and record the angle θ between the wooden rod and the bench. θ = .....................................................° (c) Change mass m to 80 g. Adjust the position of the spring and string so that the length L is the same as in (b)(i) and the string is horizontal. Repeat (b)(ii) and (b)(iii). h = ...................................................... θ = .....................................................° [1] (d) (i) Copy your value of L from (b)(i). L = ...................................................... (ii) Change m and repeat (b)(ii) and (b)(iii) until you have six sets of values of m, h and θ. For each value of m, adjust the position of the spring and string so that L is the same as in (d)(i) and the spring is horizontal. Include your values from (b) and (c). h Also include values of in your table. cos θ [10] h (e) (i) Plot a graph of on the y-axis against m on the x-axis. [3] cos θ (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 h, θ and m are related by the equation h = Am + B cos θ 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 for L to the nearest mm, with unit. [1] (c) Second value of h > first value of h. [1] (d) (ii) Six sets of readings of m, h and θ scores 5 marks, five sets scores 4 marks etc. [5] Help from Supervisor –1. Incorrect trend –1. Correct trend is h increases as m increases. Range: [1] Range of values to include mmin < 60 g and mmax > 80 g. 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. h / cos θ (cm). Consistency: [1] All values of h must be given to the nearest mm. Significant figures: [1] Every value of h / cos θ must be given to 2 or 3 significant figures only. Calculation: [1] Values of h / cosθ 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 10 g in the m direction of 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 correct (e.g. m kg–1 or cm g–1) and unit for B correct (m or cm or mm). [1]

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2 In this experiment, you will investigate the motion of a loaded wooden rod. (a) (i) Set up the apparatus as shown in Fig. 2.1. stands rod of clamp boss rod of clamp boss long string loop spring wooden rod z x y mass m1 mass m2 ʜ 6 cm bench Fig. 2.1 Support the wooden rod by passing it through the loop of the spring and the long string loop. Mass m1 should be 200 g and mass m2 should be 100 g. The bottom of mass m1 should be approximately 6 cm above the bench. (ii) Adjust the apparatus until the wooden rod is balanced and horizontal. The spring and long string loop should be vertical. (iii) Measure and record the distances x, y and z as shown in Fig. 2.1, where x is the distance between the loop above m1 and the spring loop, y is the distance between the spring loop and the long string loop, z is the distance between the long string loop and the loop above m2. x = ...................................................... y = ...................................................... z = ...................................................... [2] (iv) Estimate the percentage uncertainty in your value of y. percentage uncertainty = ................................................. [1] (b) Calculate C where C = m1(x + y )2 + m2z 2. C = ................................................. [1] (c) (i) Pull the left side of the wooden rod down by 5 cm. Release the wooden rod and watch the movement. The wooden rod will move up and down again, completing a cycle as shown in Fig. 2.2. one complete cycle Fig. 2.2 (ii) The time taken for one complete cycle is T. By timing several of these complete cycles, determine an accurate value for T. T = ................................................. [2] (iii) Calculate T 2. T 2 = ...................................................... (iv) Justify the number of significant figures that you have given for your value of T 2. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................. [1]

Mark scheme: 2 (a) (iii) Values of x, y and z to the nearest mm with unit. [1] Value of z > value of x. [1] (iv) Absolute uncertainty in y of 1 mm to 4 mm and correct method of calculation to obtain percentage uncertainty. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if working is clearly shown. [1] (b) Correct calculation of C with consistent unit. [1] (c) (ii) Value for T with unit in range 5.0 s > T > 0.5 s. [1] Evidence of repeat readings for T. [1] (iv) Justification for significant figures in T2 linked to significant figures in the (raw) times. [1] (d) Second values of x, y and z. Value of y within 5 mm of value in (a)(iii). [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) Valid comment consistent with the calculated values of k, testing against a criterion specified by the candidate. [1] (f) (i) Limitations (4 max.) (ii) Improvements (4 max.) Do not credit A Not enough readings to draw a Take many readings (for different “Repeat readings” on its conclusion masses) and plot a graph/ own/ obtain more k values and compare few readings/ only one reading/ not enough readings for an accurate result/ take more readings and (calculate) average k B Rod is bent when loaded Use smaller masses/ Just “rod is bent”/ rigid/stiff/thick rod shorter rod C Difficult to get horizontal Use a spirit level or named instrument. D Difficult to measure distances with Add a scale on rod/ Parallax reason e.g. rod unstable/awkward use travelling microscope/ with metre rule/rod moves/holding clamp ruler Do not award if reason ruler mid-air given is bent rod. E y not constant with a reason e.g. Cut groove or drill hole in wooden spring/loop moves around during rod/ oscillations tape to wooden rod F Difficult to judge the start/end of an (Fiducial) marker at centre/ More oscillations/ oscillation video and timer/view frame by high speed camera/ or frame/ reaction time/ Difficult to judge when to start/stop motion sensor placed below/above human error the stopwatch G Oscillation in more than one Wind/draughts/ plane/irregular oscillations switch off air conditioning/ close doors and windows

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