Cambridge A Level Physics 9702 — 2019 May/June Paper 3 · Variant 3

1 In this experiment, you will investigate the oscillations of a metre rule. (a) • Set up the apparatus as shown in Fig. 1.1. • Attach the beaker to the block of wood using modelling clay. • The distance between the centre of each 150 g mass and the nearest end of the rule is x. Adjust the apparatus so that the value of x is approximately 20 cm and the rule is balanced on the beaker, as shown in Fig. 1.1. x x 150 g mass metre rule beaker modelling clay block of wood bench Fig. 1.1 • Record x. x = ......................................................... [1] (b) • Pull one end of the rule down through a short distance. • Release the end of the rule so that it oscillates. • Determine the period T of these oscillations. T = ......................................................... [2] (c) Reduce x by changing the positions of the 150 g masses on the rule. Measure and record x and T. Repeat until you have five sets of values. Record your results in a table. [7] (d) (i) Plot a graph of T 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] (e) It is suggested that the quantities T and x are related by the equation T = Px + Q where P and Q are constants. Using your answers in (d)(iii), determine the values of P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] (f) For one particular value of x, the value of T is the same as when there are no masses on the rule. • Remove the masses from the rule. • Balance the rule on the beaker and repeat (b). T = ............................................................... • Use your value of T and answers in (e) to calculate this value of x. Give your answer to three significant figures. x = ......................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of x in the range 18.0–22.0 cm with unit. 1 1(b) Value of T in the range 2.50–4.50 s with unit. 1 Evidence of at least two readings of nT where n ⩾ 2. 1 1(c) Five sets of readings of x and T (different values) showing the correct trend and without help from the Supervisor scores 4 marks, four sets scores 3 marks etc. 4 Range: xmin ⩽ 5.0 cm. 1 Column headings: Each column heading must contain a quantity, a unit and a separating mark 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 must be given to the nearest mm only. 1 1(d)(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 correctly 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 observations in the table (at least 4) must be plotted on the grid. Trend of points on graph must be correct. It must be possible to draw a straight line that is within ±2.0 cm (to scale) of all the plotted points on the x-axis. 1 Question Answer Marks 1(d)(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. If there are 5 or more points, allow one anomalous point only if clearly indicated by the candidate. Lines must not be kinked or thicker than half a small square. 1 1(d)(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 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(e) Value of P = candidate’s gradient and value of Q = candidate’s intercept. The values must not be fractions. 1 Units for P (s m–1, s cm–1 or s mm–1) and Q (s) correct. 1 1(f) Correct calculation of x [= (T – Q) / P] from values of T, P and Q and consistent sign. 1 Final answer for x given to three significant figures. 1

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2 In this experiment, you will investigate the path of a bouncing ball. (a) (i) • Set up the apparatus as shown in Fig. 2.1. stand boss clamp dot board θ bench Fig. 2.1 • Support the board using the clamp. • The dot on the board should be facing upwards and be close to the top end of the board. The angle θ between the board and the bench should be approximately 25°. Measure and record θ. θ = ........................................................° [1] (ii) Calculate (sin 2θ)(cos 2θ). (sin 2θ)(cos 2θ) = ......................................................... [1] (iii) Justify the number of significant figures that you have given for your value of (sin 2θ)(cos 2θ). ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (b) • Use the G-clamp to support the card vertically, as shown in Fig. 2.2. paper card G-clamp Fig. 2.2 • Position the card at the lower edge of the board, as shown in Fig. 2.3. card supported by G-clamp (G-clamp not shown) paper d dot A Fig. 2.3 • Draw a horizontal line on the paper at the same height above the bench as the dot. Label this line A. • The horizontal distance between the line A and the dot is d. Measure and record d. d = ......................................................... [2] (c) (i) • Hold the ball vertically above the dot on the board, as shown in Fig. 2.4. • Release the ball so that it bounces from the board and strikes the card. • Continue releasing the ball from different heights until the ball strikes the line A. • The height of the ball above the dot is h. ball h dot A Fig. 2.4 Measure and record h. h = ......................................................... [1] (ii) Estimate the percentage uncertainty in your value of h. percentage uncertainty = ......................................................... [1]

Mark scheme: 2(a)(i) 1 2(a)(ii) Correct calculation of (sin 2θ)(cos 2θ). 1 2(a)(iii) Justification for s.f. in (sin 2θ)(cos 2θ) linked to s.f. in θ or angle. 1 2(b) Value of d to the nearest mm with unit. 1 Value of d in the range 35.0 cm < d < 45.0 cm. 1 2(c)(i) Value of h with unit in the range 10.0 cm < h < 100.0 cm. 1 2(c)(ii) Percentage uncertainty in h based on absolute uncertainty of 0.5–5.0 cm. 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(d) Second values of θ and d. 1 Second value of h. 1 Quality: Second value of h greater than first value of h. 1 2(e)(i) Two values of k calculated correctly. 1 2(e)(ii) Valid comment consistent with calculated values of k, testing against a criterion stated by the candidate. 1 Question Answer Marks 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to set θ (or angle) with a reason e.g. board moves/is tilted or moves when clamp tightened. C Difficult to locate A or B because difficult to judge the horizontal. D Difficult to measure d with reason e.g. parallax error, moving card, ruler held by hand, card not perpendicular to bench, card not vertical. E Difficult to release/align the ball either directly above the dot or without applying a force or in exactly the same place when repeated. F Difficult to find/measure h with a reason e.g. parallax error, ruler held by hand, ball held by hand, ruler not vertical, uneven bounce of ball. G Difficult to judge whether the ball hits the line or A or B. 1 mark for each point up to a maximum of 4. 4 Question Answer Marks 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). B Improved method to make ramp more stable or θ easy to adjust e.g. use two stands, use pile of books (that can be moved), lab jack. C Improved method of locating A or B e.g. detailed use of spirit level/set squares/ruler(s). D Improved method of measuring d e.g. clamp a ruler horizontally or to measure d, trigonometry with detail, clamp top of card, use stiffer or thicker card. E Improved method of aligning or releasing ball e.g. launch guide, plumb line, short tube (with card), clamp guide vertically, method of fixing release point, hang ball by string and cut/burn. F Improved method to find h e.g. clamp ruler vertically or to measure h (allow use of set square on bench and ruler (with detail)). G Improved method of judging where the ball hits the card e.g. paint ball, coloured screen, sticky screen or video/film (and replay) linked to ball hitting card. 1 mark for each point up to a maximum of 4. 4

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