Cambridge A Level Physics 9702 — 2018 May/June Paper 3 · Variant 1

1 In this experiment, you will investigate the oscillations of a mass. (a) Set up the apparatus as shown in Fig. 1.1. stands boss rod of clamp spring boss rod of clamp A string loop metre rule string loop d s mass M bench Fig. 1.1 • Hang mass M from the string loop near the end of the metre rule. • Ensure that the metre rule is pushing up against the rod of clamp A at approximately the 24 cm mark. • The distance between the rod of clamp A and the string attached to the spring is d. Adjust the position of the stand holding the spring so that d is approximately 30 cm. • Adjust the height of the clamps until the rule is horizontal. Ensure that the spring is vertical. • Measure and record d. d = ............................................................... • The distance between the rod of clamp A and the string supporting M is s. Measure and record s. s = ............................................................... [1] (b) • Pull M down through a short distance. • Release M so that it oscillates. • Determine the period T of these oscillations. T = .......................................................... [1] (c) • Without moving the stands, slide the rule horizontally through the string loop so that d remains constant but s changes. • Adjust the height of the clamps until the rule is horizontal. Ensure that the spring is vertical. • Measure and record s. s = ............................................................... • Repeat (b). T = ............................................................... [1] (d) Vary s and repeat (c) until you have five sets of values of s and T. You may include your previous sets of readings. Record your results in a table. Include values of T 2 in your table. [9] (e) (i) Plot a graph of T 2 on the y-axis against s 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) It is suggested that the quantities T and s are related by the equation T 2 = Ps + Q where P and Q are constants. Using your answers in (e)(iii), determine the values of P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of raw d to nearest mm with unit and in the range 29.0–31.0 cm. 1 1(b) Value of T in the range 0.8–2.0 s with unit and evidence of at least two sets of nT where n ⩾ 5. 1 1(c) Second set of values of s and T. 1 1(d) Five sets of readings of s and time (different values) with the correct trend and without help from the Supervisor scores 4 marks, four sets scores 3 marks etc. 4 Range: at least one value of s ⩽ 70.0 cm and at least one value of s ⩾ 85.0 cm 1 Column headings: 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. s / cm, T / s, T2 / s2 or T2 (s2). 1 Consistency: All raw time values must be given to 0.1 s or all given to 0.01 s. 1 Significant figures: All values of T2 must be given to the same number of s.f. as (or one more than) the number of s.f. in the raw value(s) of time. If raw times are given to 0.01 s, allow T2 to be recorded to 1 s.f. less than the raw times. 1 Calculation: Values of T2 are correct. 1 Question Answer Marks 1(e)(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 (no “blobs”). Points must be plotted to an accuracy of half a small square. 1 Quality: All points in the table must be plotted on the grid for this mark to be awarded. It must be possible to draw a straight line that is within ± 2.5 cm (to scale) on the s axis (normally x axis) of all plotted points. 1 1(e)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate’s line (at least 4 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. There must be at least four points left after the anomalous point is disregarded. Line must not be kinked or thicker than half a small square. 1 1(e)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. The method of calculation must be correct. Do not allow ∆x / ∆y. Both read-offs must be accurate to half a small square in both the x and y directions. Sign of gradient must match graph. 1 y-intercept: Correct read-off from a point on the line substituted correctly into y = mx + c or an equivalent expression. 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 s = 0, accurate to half a small square in y direction. 1 Question Answer Marks 1(f) Value of P = candidate’s gradient and value of Q = candidate’s intercept. The values must not be fractions. 1 Unit for P correct (e.g. s2 m–1 or s2 cm–1 or s2 mm–1). and Unit for Q is s2. 1

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2 In this experiment, you will investigate the oscillations of a magnet. (a) You have been provided with a metal plate. • Use tape to secure the plate at the edge of the bench as shown in Fig. 2.1. tape plate tape edge of bench Fig. 2.1 • Use more tape to secure one of the paper strips to the bench so that it covers the plate, as shown in Fig. 2.2. TOP VIEW OF BENCH plate under paper paper strip tape tape A B edge of bench Fig. 2.2 You have been provided with a bar magnet attached to a string. • Set up the apparatus as shown in Fig. 2.3. clamp boss split cork stand string § 55 cm bar magnet x bench plate covered by paper Fig. 2.3 • The distance between the bottom of the split cork and the bottom of the magnet should be approximately 55 cm. • The distance between the bottom of the magnet and the paper strip is x. Adjust the height of the magnet so that x is approximately 3 mm. • Measure and record x. x = .......................................................... [1] (b) • Move the stand until the magnet hangs with one edge vertically above line A, as shown in Fig. 2.4. magnet paper string A Fig. 2.4 • Pull the magnet to the right, keeping the string straight, until the same edge of the magnet is above line B, as shown in Fig. 2.5. B Fig. 2.5 • Release the magnet. The magnet will oscillate. • Draw a line on the paper at the position of the edge of the magnet after 30 complete oscillations. • Label this line C. The distance BC is y as shown in Fig. 2.6. A C B y Fig. 2.6 • Measure and record y. y = .......................................................... [2]

Mark scheme: 2(a) Value of x with unit and in the range 1.0–5.0 mm. 1 2(b) All value(s) of raw y to nearest mm with unit. 1 Evidence of repeat values of y. 1 2(c) Absolute uncertainty in y 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 find percentage uncertainty. 1 2(d) Second value of x. 1 Second value of y. 1 Quality: second value of y < first value of y. 1 2(e)(i) Two values of k calculated correctly. 1 2(e)(ii) Valid comment consistent with the calculated values of k, testing against a criterion stated by the candidate. 1 2(f)(i) Value of y. 1 2(f)(ii) Correct calculation of x. 1 2(f)(iii) Justification for s.f. in x linked to s.f. in y. 1 2(g)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficulty with alignment at A with a reason e.g. string twists/magnet will not settle/magnet continually moves/draughts or air conditioning disturb magnet. C Difficulty with finding position C or position after 30 oscillations or finding y with a reason e.g. magnet only stays at position C for a short time/difficult to estimate where magnet will stop/difficult to judge the end of an oscillation/parallax. D Difficulty linked to x with a reason e.g. metre rule (too large or not precise enough/large percentage uncertainty in x/value of x is small/ adjustment difficult or clumsy with clamp and cork/angled lower surface of magnet. E Difficulty with the oscillation e.g. magnet rotates while swinging/wrong mode of oscillation/magnetic stand attracts the magnet affecting its motion. 1 mark for each point up to a maximum of 4. 4 2(g)(ii) A Take many readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Improved method of alignment with A e.g. valid improvement to suspension e.g. nylon thread/wire/double point of suspension/switch off AC/windshield. C Improved method of locating C e.g. use a scale/use of a pointer with detail of how pointer is used e.g. attached to magnet/use to refine position of C. D1 Improved method to adjust x e.g. scissor jack/rearrange suspension to use screw thread on clamp. D2 Improved method to measure x e.g. travelling microscope/vernier or digital calipers/use of thin spacers e.g. sheets of paper/shim. E Use a wooden or plastic stand i.e. a named non-magnetic material. 1 mark for each point up to a maximum of 4. 4

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