Cambridge A Level Physics 9702 — 2019 May/June Paper 3 · Variant 4

1 In this experiment, you will investigate the equilibrium position of a cardboard triangle. (a) • Assemble the apparatus as shown in Fig. 1.1, with the nail passing through the hole marked A and the wire hook passing through one of the remaining holes. • Ensure that the nail is held securely in the clamp and that the cardboard triangle can swing freely on the nail. nail clamp boss x A cardboard triangle α β stand wire hook modelling clay Fig. 1.1 (not to scale) • The angle of the lower corner of the card is α, as shown in Fig. 1.1. • Measure and record α. α = ............................................................. ° • Calculate the value of α 2. α = ............................................................. ° 2 [1] (b) • The angle between the wire hook and the edge of the card is β, as shown in Fig. 1.1. Measure and record β. β = ............................................................. ° • The distance between the hole with the wire hook in it and the hole furthest from A is x, as shown in Fig. 1.1. Measure and record x. x = ..........................................................cm [1] (c) Move the wire hook to another hole and repeat (b) until you have six sets of values of β and x. Record your results in a table. α Include values of − in your table. tan(β 2) [10] α(d) (i) Plot a graph of − on the y-axis against x on the x-axis. [3] tan(β 2) (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 β, α and x are related by the equation α − = Px + Q tan(β 2) where P and Q are constants. Use your answers in (d)(iii) to 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) 1 1(b) Value of β > α / 2. 1 1(c) Six sets of readings of β and x (different values) showing the correct trend (β increases as x decreases) and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: xmin = 0.0 cm and xmax ⩾ 6.5 cm. 1 Column headings: Each column heading must contain a quantity, a unit and a separating mark where appropriate. The heading for tan (β – α / 2) must have no unit. The presentation of the quantity and unit must conform to accepted scientific convention e.g. β / °. 1 Consistency: All raw values of x must be given to the nearest mm. 1 Significant figures: All values of tan (β – α / 2) should be to 2 or 3 significant figures. 1 Calculation: Values of tan (β – α / 2) calculated correctly. 1 Question Answer Marks 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 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 5) must be plotted on the grid. Scatter of plots must be no more than ±0.5 cm (to scale) from a straight line in the x direction. 1 1(d)(ii) Line of best fit: Judge by 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. Allow one anomalous point only if clearly indicated by the candidate. Lines must not be kinked or thicker than half a 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 Question Answer Marks 1(e) Value of P = candidate’s gradient and value of Q = candidate’s intercept. 1 Unit for P correct (e.g. cm–1) and consistent with results and no unit for Q. 1

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2 In this experiment, you will investigate the forces on an irregularly shaped object. (a) • Position the wooden strip on the prism so that it is balanced. Make a small mark on the side of the strip where it rests on the prism, as shown in Fig. 2.1. mark wooden strip prism wooden block bench Fig. 2.1 • Place the beaker under the wooden strip. • Hang the larger rock inside the beaker at a distance of 30.0 cm from the mark, then balance the strip by placing the mass on the other side of the mark, as shown in Fig. 2.2. 30.0 cm c mass string beaker rock Fig. 2.2 • The distance between the centre of the mass and the mark is c. Measure and record c. c = ......................................................... [2] (b) • Pour water into the beaker until the rock is completely immersed. • Balance the strip by moving the position of the mass, as shown in Fig. 2.3. d beaker water Fig. 2.3 • Ensure that the rock is completely immersed and is not touching the bottom of the beaker. • The distance between the centre of the mass and the mark is d. Measure and record d. d = ......................................................... [1] (c) Estimate the percentage uncertainty in your value of d. percentage uncertainty = ......................................................... [1] (d) • Carefully remove the rock from the water. • Pour the water from the beaker into the jug. • Replace the rock with the smaller rock, ensuring that it is 30.0 cm from the mark. • Balance the strip by placing the mass on the other side of the mark, as shown in Fig. 2.2. • Measure and record c. c = ............................................................... • Repeat (b). d = ............................................................... [3] (e) It is suggested that the relationship between c and d is k(c − d) = c where k is a constant. (i) Using your data, calculate two values of k. first value of k = ............................................................... second value of k = ............................................................... [1] (ii) Justify the number of significant figures that you have given for your values of k. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1]

Mark scheme: 2(a) Value of c to the nearest mm, with unit. 1 Value of c in the range 20.0–40.0 cm. 1 2(b) Value of d < c. 1 2(c) Percentage uncertainty in d based on an absolute uncertainty of 2–10 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(d) Second value of c. 1 Second value of d. 1 Quality: Second c < first c and second d < first d. 1 2(e)(i) Two values of k calculated correctly. 1 2(e)(ii) Justification based on s.f. in c and (c – d). 1 2(e)(iii) Valid comment relating to the calculated values of k, testing against a criterion specified by the candidate. 1 2(f) Correct calculation of ρrock. 1 ρrock in range 2100–3200 kg m–3, with unit. 1 Question Answer Marks 2(g)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to balance strip/prism moves/strip slips/strip slides/strip moves on prism. C Difficult to measure c or d with reason e.g. difficult to locate centre of (the) mass/parallax error. D Wet string changes mass/weight. E Volume of string not taken into account/string displaces water/upthrust on string or Mass of string not taken into account. F Difficult to set/measure the position of the rock because of thick string. 1 mark for each point up to a maximum of 4. 4 2(g)(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 of balancing strip e.g. groove under strip/flatten top of prism/method of fixing prism or wooden block. C Improved method of measuring c or d e.g. scale markings on strip/suspend mass under strip. D Method of reducing water absorbed by string e.g. use waterproof string/nylon/wire/other named (suitable) material. E Method of reducing volume/mass of string e.g. thin(ner) string. F Use thin(ner) string (allow ‘thin(ner) string’ only once in total). 1 mark for each point up to a maximum of 4. 4

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