Cambridge A Level Physics 9702 — 2019 Oct/Nov Paper 3 · Variant 3

1 In this experiment, you will investigate the equilibrium of a metre rule. (a) You have been provided with a metre rule with a 100 g mass attached to it. • Set up the apparatus as shown in Fig. 1.1. boss string loop rod of clamp 100 g mass y string x metre rule loop mass P stand bench Fig. 1.1 The distance between the end of the rule and the string loop from which mass P is suspended is x, as shown in Fig. 1.1. The distance between the same end of the rule and the string loop suspended from the rod of the clamp is y. • Position mass P so that x is approximately 30 cm. • Without changing x, adjust the position of the rule until it balances. • Measure and record x and y. x = ............................................................... y = ............................................................... [2] (b) Change x. Adjust the position of the rule until it balances. Measure and record x and y. Repeat until you have six sets of values. Record your results in a table. [8] (c) (i) Plot a graph of y on the y-axis against x 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] (d) It is suggested that the quantities y and x are related by the equation y = Ax + B where A and B are constants. Using your answers in (c)(iii), determine the values of A and B. Give appropriate units. A = ............................................................... B = ............................................................... [2] (e) Theory suggests that 2M A = 3M + Q where M is the mass of the metre rule and Q = 0.100 kg. Determine a value for M. Give your answer to three significant figures. Include an appropriate unit. M = ......................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of x in the range 28.0–32.0 cm with unit. 1 Value of y in the range 45.0–55.0 cm. 1 1(b) Six sets of readings of x and y (different values) showing the correct trend and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: Must include one value of x ⩽ 10.0 cm and one value of x ⩾ 50.0 cm. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of the quantity and unit must conform to accepted scientific convention e.g. x / m. 1 Consistency: All raw values of x and y must be given to the nearest mm. 1 1(c)(i) Axes: 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 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. 1 Plotting of points: 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. 1 Quality: All points in the table (at least 5) must be plotted on the grid. Trend of points on graph must be positive. All points must be within ±1.0 cm (to scale on the axis with the y values) of a straight line. 1 Question Answer Marks 1(c)(ii) Line of best fit: 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. One anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate. There must be at least 5 points left after the anomalous point is disregarded. Line must not be kinked or thicker than half a small square. 1 1(c)(iii) Gradient: 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. The method of calculation must be correct e.g. not ∆x / ∆y. The sign of the gradient on the answer line must match the graph. 1 y-intercept: 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 Intercept read directly from the graph with read-off at x = 0 accurate to half a small square. 1 1(d) Value of A = candidate’s gradient and value of B = candidate’s intercept. The values must not be fractions. 1 A has no unit and unit for B correct (m, cm or mm). 1 1(e) Correct calculation of M with a consistent unit. 1 Answer on the answer line to 3 significant figures. 1

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2 In this experiment, you will investigate the motion of a magnet connected to some springs. (a) (i) You have been provided with two magnets A and B and three connected springs. • Use the tape to attach magnet A to the springs as shown in Fig. 2.1. N A magnet A springs tape Fig. 2.1 • Set up the apparatus as shown in Fig. 2.2, with the N poles of magnets A and B facing each other. wooden rod boss springs stand magnet A N pole x N pole magnet B held in G-clamp bench Fig. 2.2 • The distance between the magnets is x. Adjust the height of the wooden rod until x is approximately 7 cm. • Measure and record x. x = ......................................................... [1] (ii) Estimate the percentage uncertainty in your value of x. percentage uncertainty = ......................................................... [1] (b) (i) • Pull magnet A down through a short distance. • Release the magnet. The magnet will oscillate. • Determine the period T1 of these oscillations. T1 = ...................................................... s [2] (ii) • Reverse magnet B in the G-clamp so that its S pole is at the top. • Adjust the position of the wooden rod until x has the same value as in (a)(i). • Determine the period T2 of the oscillations of magnet A. T2 = ...................................................... s [1] (iii) Calculate T2 − T1. T2 − T1 = ...................................................... s [1] (c) • Reverse magnet B so that its N pole is at the top. • Adjust the position of the wooden rod until x is approximately 10 cm. • Measure and record x. x = ............................................................... • Repeat (b) using this value of x. T1 = ............................................................ s T2 = ............................................................ s T2 − T1 = ............................................................ s [3] (d) It is suggested that the relationship between T1, T2 and x is k T2 − T1 = 3 x where k is a constant. (i) Using your data, calculate two values of k. first value of k = ............................................................... second value of k = ...............................................................

Mark scheme: 2(a)(i) Value of x in the range 6.5–7.5 cm to the nearest mm with unit. 1 2(a)(ii) Percentage uncertainty in x based on absolute uncertainty in the range 2–4 mm. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(b)(i) Value of T1 in the range 0.4–1.0 s. 1 At least two values of nT recorded where n ⩾ 5. 1 2(b)(ii) Value of T2 greater than T1. 1 2(b)(iii) Correct calculation of T2 − T1. 1 2(c) Second value of x. 1 Second values of T1 and T2. 1 Quality: Second value of |T2 − T1| < first value of |T2 − T1|. 1 2(d)(i) Two values of k calculated correctly. 1 2(d)(ii) Justification for s.f. in k linked to s.f. in x and (T2 – T1). 1 2(d)(iii) Valid comment consistent with calculated values of k, testing against a criterion stated by the candidate. 1 Question Answer Marks 2(e)(i) A Too few readings/(only) two readings not enough to draw a (valid) conclusion (not ‘not enough for accurate results’, ‘few readings’). B Problem with attaching spring to magnet e.g. tape not sticky enough, magnet falls from tape or Problems with additional modelling clay falling off magnet. C Difficult to line up magnets (because they repel). D Difficulty setting or measuring x with a reason e.g. holding metre rule by hand/metre rule or magnet moves/metre rule not vertical/parallax error/magnet is tilted so x varies across the width of the magnet/difficult to adjust boss so that x has the constant value. E (T2 – T1) is short or Percentage uncertainty in (T2 – T1) is large or Difficult to judge start of/end of/complete oscillation. F Others modes of oscillation e.g. magnet swinging or Magnets are attracted/stick to the stand (metal rod) and/or G-clamp/metal table. 1 mark for each point up to a maximum of 4. 4 Question Answer Marks 2(e)(ii) A Take more readings and plot a graph or take more readings and compare k values (not ‘repeat readings’ on its own). B Better method of attaching magnet to spring system e.g. glue spring to magnet/stickier tape/magnet with hook/attach string or Improved method of adding weight to magnet e.g. use adhesive putty/tape. C Put magnets in a (transparent) tube. D Improved method of measuring x e.g. place a mm grid behind magnets/clamp metre rule/use set square between ruler and bench/plumb-line to check ruler vertical/use a lab jack to raise magnet B/use travelling microscope. E Improved method of timing e.g. video/film/record with timer/view frame-by-frame, fiducial marker at centre of oscillation, force meter attached to springs. F Use wooden/plastic stand/longer wooden rod or Another named method of fixing magnet B to bench e.g. adhesive putty. 1 mark for each point up to a maximum of 4. 4

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