Cambridge A Level Physics 9702 — 2018 May/June Paper 3 · Variant 2

1 In this experiment, you will investigate the motion of a rolling sphere. (a) (i) • Assemble the apparatus as shown in Fig. 1.1. The top end of the track is a distance d above the bench. The initial value of d should be approximately 5 cm. stand SIDE VIEW clamp wooden tape strip target track wooden strip d bench Blu-Tack TOP VIEW wooden strip boss target wooden strip Blu-Tack A 50.0 cm label A wooden strip Fig. 1.1 • Ensure that the distance between the bottom of the track and the target wooden strip is 50.0 cm. • Place the sphere on the track and hold it gently against the tape, as shown in Fig. 1.2. sphere h bench Fig. 1.2 • Measure and record the height h of the top of the sphere above the bench. h = .......................................................... [1] (ii) • Release the sphere. • Measure and record the time t from release for the sphere to reach the target. t = .......................................................... [2] (b) Change d and repeat (a) until you have six sets of values of h and t. Do not use values of d greater than 10 cm. Ensure that the distance from the bottom of the track to the target is always 50.0 cm. 1 Record your results in a table. Include values of in your table. t2 [9] 1(c) (i) Plot a graph of on the y-axis against h on the x-axis. [3] t2 (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 t and h are related by the equation 1 = ah + b t2 where a and b are constants. Use your answers in (c)(iii) to 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: 1(a)(i) Value of h to nearest mm, with unit. 1 1(a)(ii) Value of t in the range 1.0–5.0 s, with unit. 1 At least two readings of t. 1 1(b) Six sets of readings of h and t showing the correct trend and without help from the Supervisor scores 4 marks, five sets scores 3 marks etc. 4 Range: tmax ⩾ 2.0 s and tmin ⩽ 1.5 s. 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. (1 / t2) / s–2. 1 Consistency: All raw values of t must be given to 0.01 s or all must be given to 0.1 s. 1 Significant figures: Significant figures for every value of 1 / t 2 same as, or one greater than, the number of s.f. of t as recorded in table. 1 Calculation: Values of 1 / t 2 calculated correctly to the number of s.f. given by the candidate. 1 Question Answer Marks 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 (no “blobs”). Plots must be accurate to within half a small square in both x and y directions. 1 Quality: All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of points must be no more than ± 0.05 s–2 from a straight line in the 1 / t2 direction. 1 1(c)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate’s line (at least 5). There must be an even distribution of points either side of the line along the full length. Allow one anomalous only if clearly indicated (i.e. circled or labelled) by the candidate. Lines 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. 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 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 x = 0 accurate to half a small square in y direction. 1 1(d) Value of a equal to candidate’s gradient and value of b equal to candidate’s intercept. 1 Unit for a correct (e.g. mm–1 s–2 or cm–1 s–2) and unit for b is s–2. 1

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2 In this experiment, you will investigate stationary wave patterns. (a) You are provided with two pieces of string of different diameters. Each piece of string has a 10 g mass attached to one end. Using the thinner string, assemble the apparatus as shown in Fig. 2.1. clamped unclamped wooden block wooden block tape bench G-clamp hacksaw blade string L 10 g mass Fig. 2.1 The length of string between the hacksaw blade and the 10 g mass is L, as shown in Fig. 2.1. Measure and record L. L = .......................................................... [1] (b) The length of hacksaw blade outside the blocks is x, as shown in Fig. 2.2. x Fig. 2.2 When the end of the hacksaw blade is moved a small distance to one side and released, the string vibrates. For certain values of x, the string vibrates in stationary wave patterns. Examples of these patterns are shown in Fig. 2.3. A B C Fig. 2.3 • Press down on the unclamped wooden block. • Move the end of the hacksaw blade a small distance to one side and release it. • Change x in small steps. Keep changing x, testing for a pattern at each step, until the pattern B with three loops is clearly produced. • Measure and record x. x = .......................................................... [2] (c) Estimate the percentage uncertainty in your value of x. percentage uncertainty = .......................................................... [1] 2L(d) Calculate the value of λ in metres, using λ = . 3 λ = ...................................................... m [1] (e) Justify the number of significant figures you have given for your value of λ. ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[1]

Mark scheme: 2(a) Value for L to nearest mm with unit and in range 50.0–75.0 cm. 1 2(b) Value for x with unit. 1 Raw value(s) of x to nearest mm and value on answer line in range 100–200 mm. 1 2(c) Absolute uncertainty in x value of 0.2–0.5 cm 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 2(d) Correct calculation of λ to the number of significant figures used by the candidate. 1 2(e) Justification linking s.f. in λ to s.f. in L. 1 2(f) Correct calculation of f. 1 2(g) Second values of L and x. 1 Quality: x increases as µ increases. 1 Second values of λ and f. 1 2(h)(i) Two values of k calculated correctly. 1 2(h)(ii) Valid comment consistent with the calculated values of k, testing against a numerical criterion specified by the candidate. 1 Question Answer Marks 2(i)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to see string pattern. C String pattern dies away quickly. D Difficult to produce exact pattern required. E Difficulty with wooden block e.g. doesn’t grip blade/hard to hold down block and oscillate blade/view pattern at same time. F Hacksaw/mass not at a node in the string pattern. 1 mark for each point up to a maximum of 4. 4 2(i)(ii) A Take many readings and plot a graph or take more values of k and compare (not “repeat readings” on its own). B Put contrasting/black/white background behind string. C Use photo/video to assess pattern or description of workable method of producing continuous oscillations. D Add a scale/marks to hacksaw blade. E Clamp/put weight on the movable wooden block. F Workable solution to allow a node e.g. move excitation point away from node/use heavier mass. 1 mark for each point up to a maximum of 4. 4

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