Cambridge A Level Physics 9702 — 2014 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will investigate the motion of masses suspended from springs. (a) (i) Set up the apparatus as shown in Fig. 1.1. boss rod of clamp spring stand mass P mass m bench Fig. 1.1 The mass P must be 200 g and must remain constant throughout the experiment. The mass m should be 250 g. (ii) Calculate and record (m – P ). (m – P ) = ..................................................[1] (b) (i) Pull both masses down through a short distance. Release both masses at the same time and watch the movement. The two masses will move up and down becoming out of step. After a time the masses will be back in step so that they reach the lowest point together. (ii) Pull both masses down through a short distance. Release both masses at the same time. Start the stopwatch when the masses are back in step and reach the lowest point together for the first time. Measure and record the time t taken for the masses to reach their lowest point together for the sixth time. t = ..................................................[1] (c) Increase m and repeat (a)(ii) and (b)(ii) until you have six sets of readings of m and t. 1 Include values of 2 and (m – P ) in your table. t [10] 1 (d) (i) Plot a graph of 2 on the y-axis against (m – P ) on the x-axis. [3] t (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] (e) It is suggested that the quantities t, m and P are related by the equation 1 2 = U (m – P ) + V t where U and V are constants. Use your answers in (d)(iii) to determine the values of U and V. Give appropriate units. U = ...................................................... V = ...................................................... [2] You may not need to use all of the materials provided.

Mark scheme: 1 (a) (ii) Value of (m – P) with consistent unit. [1] (b) (ii) 10.0 s < t < 60.0 s, with unit. If out of range allow Supervisor’s value ± 5.0 s. [1] (c) Six sets of readings of m and t scores 5 marks, five sets scores 4 marks etc. [5] Incorrect trend –1. Help from Supervisor –1. Range: [1] mmax > 360 g. Column headings: [1] Each column heading must contain a quantity and a unit. The unit must conform to accepted scientific convention e.g. 1 / t2 / s–2 or 1/t2 (s–2). 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 1 / t2 must be given to the same s.f. as (or one more than) the s.f. in raw t. Calculation: [1] Values of 1 / t2 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 must be no more than three large squares apart. Plotting: [1] All observations in the table must be plotted on the graph grid. Work to an accuracy of half a small square in both the x and y directions. Diameter of plotted points must be ≤ half a small square (no “blobs”). Quality: [1] All points in the table must be plotted (at least 5) for this mark to be awarded. Judge by the scatter of all points about a straight line. All points must be ± 0.01 kg (± 10 g) from a straight line in the (m – P) direction. (ii) Line of best fit: [1] Judge by balance of all points on the grid (at least 5 points) about the candidate’s line. 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. Lines must not be kinked or thicker than half a small square. (iii) Gradient: [1] The hypotenuse of the triangle should be greater than half the length of the line drawn. Both read-offs must be accurate to half a small square in both the x and y directions. y-intercept: [1] Either: Check 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) U = value of candidate’s gradient and V = value of candidate’s intercept. [1] Do not allow a value presented as a fraction. Unit for U (s–2 kg–1 or s–2 g–1) and V (s–2). [1] [Total: 20]

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2 In this experiment, you will investigate the motion of a plastic cup in water. (a) You have been provided with two plastic cups labelled C and D. Cup C has had part of the base removed. Cup D has had all of the base removed. Measure and record the thickness x of the plastic of the two cups. x = ..................................................[1] (b) (i) Place cup C on the grid below and draw around the hole with the pencil. Use the grid to determine the area A of the hole in cup C. 1 cm2 A = ...........................................cm2 [1] (ii) Estimate the percentage uncertainty in your value of A. percentage uncertainty = ..................................................[1] (iii) Calculate the volume V of the plastic removed to make the hole, where V = A x. V = ..................................................[2] (iv) Justify the number of significant figures that you have given for your value of V. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1] (c) (i) Using tape, attach the mass to cup C, as shown in Fig. 2.1. cup C mass tape Fig. 2.1 (ii) Hold the cup so that it rests on the surface of the water in the bucket as shown in Fig. 2.2. water bucket Fig. 2.2

Mark scheme: 2 (a) Raw value(s) for x to nearest 0.01 mm or 0.001 mm, with unit. [1] 0.10 mm < x < 0.30 mm. If outside this range, allow Supervisor’s value ± 0.10 mm. (b) (i) Value of A in the range 7.0 cm2 – 15.0 cm2. There must be a circle drawn on the grid. [1] (ii) Estimate of percentage uncertainty based on absolute uncertainty in A in range 0.25 cm2 – 2.0 cm2 and method of calculation correct. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. [1] (iii) Correct calculation of V. [1] Correct and consistent unit. [1] (iv) Correct justification of s.f. in V linked to significant figures in x and A. [1] (c) (iii) Value of T in the range 1.0 s – 10.0 s with unit. [1] (d) Second value of A. [1] Evidence of measurement of repeat values of T. [1] Quality: Second value of T < first value of T. [1] (e) (i) Correct calculation of two values of k. [1] (ii) Valid comment consistent with the calculated values of k, testing against a stated criterion. [1] (f) (i) Limitations (4 max.) (ii) Improvements (4 max.) Do not credit A Two readings are not enough to Take many readings (for ‘Not enough (repeat) draw a conclusion different diameters) and plot a readings’ / ‘too few readings’ / graph / take more readings and ‘two readings’ on its own compare k values B Difficult to measure A, with Improved method for measuring Use different cup e.g. harder / reason e.g. jagged circle / cup A (e.g. put base of cup in ink stronger cup moves when drawing circle and use as stamp on grid) or: improved method for cutting circle e.g. circle cutter / hot wire / laser cutter C Effect of cup loaded on one side Method to balance cup e.g. use Put mass on bottom of cup e.g. movement lopsided / does two equal masses on either side not fall vertically / cup hits sides Use a wider bucket on the way down D Large (percentage) uncertainty Use video / film / record / (camera High speed or slow-motion in t (because times are short) + playback) with timer / view cameras unless linked to frame-by-frame. playback Method to increase length of time e.g. taller container, smaller mass, smaller hole (for C) E Difficult to judge when cup hits Use transparent / clear bucket bottom F Thickness of base different from rim / plastic deformed when measuring thickness Do not credit: Use a computer / data loggers / sensors Use an assistant Force on release Cup heavier due to water droplets [Total: 20]

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