Cambridge A Level Physics 9702 — 2022 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate the stability of a cylinder. (a) (i) ● Use some of the sheets of paper to make a pile of approximate thickness 3 mm. ● Using the calipers, measure and record the thickness T of the pile. T = ......................................................... [1] (ii) ● Position the apparatus on the bench as shown in Fig. 1.1. bottle book pile of board sheets of paper bench w Fig. 1.1 ● Measure and record the width w of the board, as shown in Fig. 1.1. w = ......................................................... [1] (b) ● Use the stand and clamp to hold the rule vertically on the bench. ● Slowly raise the end of the board, as shown in Fig. 1.2. clamp rule boss stand z Fig. 1.2 ● Measure and record the height z of the raised end of the board when the bottle rolls over the pile of paper. z = ............................................................... ● Calculate θ using z θ = sin–1( w). θ = ............................................................... [1] (c) Change the number of sheets of paper in the pile. Measure T and z. Repeat until you have six sets of values of T and z. Record your results in a table. Include values of θ and cos θ in your table. Give your values of cos θ to three significant figures. [9] (d) (i) Plot a graph of cos θ on the y-axis against T 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) It is suggested that the quantities θ and T are related by the equation cos θ = a – bT where a and b are constants. Using your answers in (d)(iii), determine the values of a and b. Give appropriate units. a = ............................................................... b = ............................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: Question Answer Marks 1(a)(i) All values of T to the nearest 0.1 mm or all values to the nearest 0.01 mm, with unit and in the range 2.50–3.50 mm. 1 1(a)(ii) Value of w with unit in the range 25.0–35.0 cm. 1 1(b) Evidence of repeated measurements of z. 1 1(c) Six sets of readings of T and z with correct trend and without help from the Supervisor scores 4 marks, five sets scores 3 4 marks, etc. Correct trend is z increases as T increases. Range: Tmin ⩽ 2.00 mm and Tmax ⩾ 9.00 mm. 1 Column headings: 1 Each column heading must contain a quantity and a unit where appropriate The presentation of quantity and unit must conform to accepted scientific convention e.g. /°; cos  must not have a unit. Consistency: 1 All values of raw z must be given to the nearest mm. Significant figures: 1 All values of cos should be to three s.f. Calculation: 1 Values of cos  calculated correctly. 1(d)(i) Axes: 1 Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). Scales must be chosen so that the plotted points occupy at least half the graph grid in both the x and y directions Axes must be labelled with the quantity that is being plotted. Scale markings must be no more than 2 cm (one large square) apart. Plotting of points: 1 All observations in the table must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square. Points must be plotted to an accuracy of half a small square in both x and y directions. Quality: 1 All points in the table must be plotted (at least 5) on the grid for this mark to be awarded. Trend of points must be negative. It must be possible to draw a straight line that is within ± 0.5 mm (to scale) on the T axis of all plotted points. 1(d)(ii) Line of best fit: 1 ‘Best fit’ is judged by the balance of all points on the grid (at least 5) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Candidates do not need to identify an anomalous point. However if there is a point off trend, it may be identified as anomalous by circling or labelling it. There must be at least 5 points left after one anomalous point is disregarded. Lines must not be kinked or thicker than half a small square. 1(d)(iii) Gradient: 1 The hypotenuse of the triangle used must be greater than 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. Method of calculation must be correct (not x / y). Gradient sign on answer line matches graph drawn. y-intercept: 1 Correct read-off from a point on the line and substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at T = 0, accurate to half a small square. 1(e) Value of a = candidate’s intercept and value of b = minus candidate’s gradient. 1 Values must not be written as fractions. Units for a (no unit) and b (mm–1, cm–1 or m–1) correct. 1

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2 In this experiment, you will investigate the force acting on a magnet. (a) (i) You have been provided with some of the apparatus already assembled, as shown in Fig. 2.1. pointer boss and clamp stand h0 bench nut Fig. 2.1 Measure and record the height h0 of the end of the pointer above the bench. h0 = ......................................................... [1] (ii) ● Attach the small magnet to the nut, as shown in Fig. 2.2. h magnet Fig. 2.2 ● Measure and record the height h of the end of the pointer above the bench. h = ......................................................... [1] (iii) ● Calculate the deflection dm caused by the magnet, using dm = h0 – h. dm = ............................................................... ● Estimate the percentage uncertainty in your value of dm. Show your working. percentage uncertainty = ........................................................... % [1] (b) (i) You have been provided with a card showing the mass m of the magnet in g. ● Determine the value of m in kg. m = .......................................................... kg ● Calculate S using mg S = dm where g is 9.81 N kg–1. S = ............................................................... [1] (ii) Justify the number of significant figures that you have given for your value of S. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (c) (i) You have been provided with a wire coil wound around a tube and connected to a component holder. ● Use the second boss and clamp to position the tube so that the magnet hangs inside the tube, as shown in Fig. 2.3. tube boss coil clamp component holder Fig. 2.3 ● Adjust the position of the tube so that the magnet is just above the coil and is not touching the walls of the tube.

Mark scheme: 2(a)(i) Value for h0, with unit, to the nearest mm and in the range 30.0–50.0 cm. 1 2(a)(ii) Value for h, smaller than h0. 1 2(a)(iii) Absolute uncertainty of 2–8 mm. 1 If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if working is clearly shown. Correct method of calculation to find percentage uncertainty. 2(b)(i) Correct calculation of S. 1 2(b)(ii) Justification for number of significant figures in S linked to significant figures in m, g and dm. 1 2(c)(i) Value for H. 1 I obtained without help from the Supervisor and with unit and to the nearest 0.01 A. 1 2(c)(ii) Second value of H. 1 Second value of I. 1 Second value of H (for larger I) smaller than first value. 1 2(d) Two values of k calculated correctly. The final k values must not be written as fractions. 1 2(e) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 20% leading to a consistent conclusion. 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B Pointer oscillates. C Difficult to measure height (of pointer) with a reason, e.g. pointer thick/rule not vertical/ruler (is held by hand so) moves. D Large percentage uncertainty in deflection / dm or deflection / dm is (very) small so uncertainty is large. E Change in height due to current / (h – H) is (very) small. F Current/ammeter reading fluctuates/changes. G Magnet hits side of tube. 1 mark for each point up to a maximum of 4. 2(f)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). 4 B Take video with a scale/ruler/grid in view (to estimate mean value) or turn off fans/air-conditioning or use wind shield/close windows/doors or add damping with method. C Improvement for measuring height, e.g. use pointed pointer/thinner pointer/pin or clamp the ruler. D Method to increase deflection dm, e.g. use heavier magnet/use less stiff spring/use longer spring. E Method to increase h – H, e.g. use larger current/use more turns on the coil or use stronger magnet. F Named method of cleaning connections/crocodile clips/end of wire, e.g. wire wool/use soldered connections. G Use wider tube (not “larger”). 1 mark for each point up to a maximum of 4.

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