Cambridge A Level Physics 9702 — 2015 Oct/Nov Paper 3 · Variant 6

1 In this experiment, you will investigate the upthrust on an object partly immersed in water. (a) Measure and record the height H of the flask, as shown in Fig. 1.1. wire loop flask + sand bench Fig. 1.1 H = ............................................ cm [1] (b) Assemble the apparatus as shown in Fig. 1.2, with the bottom of the flask approximately 4 cm below the water surface. newton-meter boss clamp flask stand container water surface 4 cm water Kw Kb bench Fig. 1.2 (c) (i) Measure and record the height hw of the water surface above the bench, as shown in Fig. 1.2. hw = ................................................. cm (ii) Measure and record the height hb of the bottom of the flask above the bench, as shown in Fig. 1.2. hb = ................................................. cm (iii) Record the newton-meter reading F. F = .............................................. N [1] (iv) Calculate x, using x = hw – hb. x = ............................................ cm [1] (d) Adjust the height of the boss and repeat (c) until you have six sets of values of hw, hb and F. For all values of hb, the water surface should be in contact with the sloping sides of the flask. Include values of x and (H – x)3 in your table. [9] (e) (i) Plot a graph of F on the y-axis against (H – x)3 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] (f) The quantities F, H and x are related by the equation F = a (H – x)3 + b 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 (a) Value of H in the range 13.0 cm to 17.0 cm. [1] (c) (iii) Value of F to nearest 0.1 N. [1] (iv) Value of x correct and in range 3.5 cm to 4.5 cm. [1] (d) Six sets of readings of hw, hb and F scores 4 marks, five sets scores 3 marks etc. [4] Incorrect trend –1. Help from Supervisor –1. Range: [1] xmax – xmin ⩾ 6.0 cm. 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 – x)3 / cm3. Consistency: [1] All values of hw and hb must be given to the nearest mm. Significant figures: [1] Significant figures for (H – x)3 must be the same as, or one greater than, the number of s.f. for (H – x). Calculation: [1] Values of (H – x)3 calculated correctly. (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 less than ± 0.2 N from a straight line in the F direction. (ii) Line of best fit: [1] Judged 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 used must be greater than half the length of the drawn line. The method of calculation must be correct. 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 in the y direction. (f) Value of a = candidate’s gradient and value of b = candidate’s intercept. [1] Unit for a is correct (e.g. N cm–3) and unit for b is correct (e.g. N). [1]

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2 In this experiment, you will investigate the motion of a flywheel rolling down a ramp. (a) You are provided with a small flywheel, as shown in Fig. 2.1. flywheel G ' axle Fig. 2.1 (i) Measure and record the diameter d of the axle. d = ............................................ cm [1] (ii) Measure and record the diameter D of the flywheel. D = ............................................ cm [1] (b) You have also been provided with a track. Set up the track with one end raised above the bench, as shown in Fig. 2.2. stand clamp l boss mark V mark K track bench Fig. 2.2 The height h should be approximately 8 cm. (i) Measure and record the length l of the track. l = ...................................................... (ii) Measure and record the height h above the bench of the raised end of the track. h = ...................................................... (iii) Measure and record the distance s between the two marks on the track. s = ...................................................... [1] (c) (i) Place the axle of the flywheel on the track at the upper mark as shown in Fig. 2.3. Release the flywheel and watch it roll down to the lower mark (the top of the flywheel may need a gentle push to start it rolling). finger axle mark mark bench Fig. 2.3 (ii) Replace the axle of the flywheel on the track at the upper mark. Take measurements to find the time t taken for the flywheel to roll from the upper mark to the lower mark. t = ..................................................[2] (iii) Estimate the percentage uncertainty in your value of t. percentage uncertainty = ..................................................[1]

Mark scheme: 2 (a) (i) All values of d to nearest 0.001 cm and in range 0.100 cm to 0.500 cm. [1] (ii) All values of D to nearest 0.1 cm. [1] (b) Values of l, h and s present. Value of h to nearest 0.1 cm and in range 7.5 cm to 8.5 cm, with unit. [1] (c) (ii) t on answer line in range 1.00 s to 20.00 s, with unit. [1] Evidence of repeated readings for t. [1] (iii) Absolute uncertainty in t in range 0.2 s to 0.5 s and correct method of calculation to obtain percentage uncertainty. If repeated readings have been taken, then the absolute uncertainty can be half the range (but not zero) if the working is clearly shown. [1] (iv) Calculation of g correct to the second s.f., with consistent unit (e.g. m s–2). [1] (d) (ii) Second values of d and t. [1] t greater for smaller d. [1] (e) (i) Two values of k calculated correctly. [1] (ii) Justification for significant figures in k linked to significant figures in t and d. [1] (iii) Valid comment consistent with the calculated values of k, tested 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 more readings and plot a “Repeat readings” conclusion graph/ on its own/ obtain more k values and few readings/ compare only one reading/ take more readings and (calculate) average k/ two readings not enough for accurate results B Parallax error when measuring Use calipers/ Rule not vertical h or D use set square as pointer when measuring h C Plastic deforms when measuring Use larger diameter axle instead larger d/diameter with tubing of tubing D Push force to start flywheel may Release mechanism, with detail/ “Force may be too vary/push force may affect time use steeper ramp large”/ start before top line E Flywheel doesn’t travel straight/ Sensible method of preventing Reduce friction/ flywheel hits (sides of) track collision, e.g. level the track mark both sides of sideways/widen the track track F Use video with timer/ Reaction time view frame by frame/ use light gates at start and end/ use longer track

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