Cambridge A Level Physics 9702 — 2018 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will investigate the extension of a spring. (a) You have been provided with a spring. Measure and record the length x0 of the unstretched coiled section of the spring, as • shown in Fig. 1.1. x0 Fig. 1.1 x0 = ...........................................................[1] (b) Set up the apparatus as shown in Fig. 1.2. • stand A boss x rod of clamp spring 90° rod of stand B ≈ 35 cm Blu-Tack protractor on wooden block θ bench Fig. 1.2 The protractor should be attached to the wooden block using some of the Blu-Tack. The height of the rod of the clamp above the bench should be approximately 35 cm. One loop of the spring should be around the rod of the clamp. The other loop of the spring should be around the rod of stand B close to the top of the rod and secured using Blu-Tack. Slide the base of stand B until the angle between the rod of stand B and the stretched • spring is 90°. The length of the coiled section of the spring is x. • The angle between the rod of stand B and the horizontal is θ. Measure and record x and θ. x = ............................................................... θ = ............................................................... Calculate e where • e = (x – x0). e = ............................................................... [1] (c) Change the height of the boss. Slide the base of stand B until the angle between the rod of stand B and the stretched spring is again 90°. Measure and record x and θ. Repeat until you have six sets of values. e Record your results in a table. Include values of e, and tan θ in your table. cos θ [10] e(d) (i) Plot a graph of on the y-axis against tan θ on the x-axis. [3] cos θ (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 e and θ are related by the equation e = N tan θ + M cos θ where N and M are constants. Using your answers in (d)(iii), determine the values of N and M. Give appropriate units. N = ............................................................... M = ............................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) 1 1(b) Value of raw θ to the nearest degree with unit and answer line value of θ < 90°. 1 1(c) Six sets of readings of x and θ (different values) with the correct trend and without help from Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: Values of θ must include one value greater than and one value less than the value of θ in (b). 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. x / cm, e / cm, e / cos θ (m), θ / °, tan θ without a unit. 1 Consistency: All raw values of x must be given to the nearest mm only. 1 Significant figures: All values of e / cos θ must be given to the same number of significant figures as (or one more than) the number of significant figures in e or θ, whichever is the smaller. 1 Calculation: Values of e / cos θ are correct. 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. Points must be plotted to an accuracy of half a small square. 1 Quality: Trend of points on graph must be negative. All points in the table (at least 5) must be plotted on the grid. It must be possible to draw a straight line that is within ±0.05 (to scale) on the tan θ axis (normally x-axis) of all plotted points. 1 1(d)(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. Allow one anomalous point only if clearly indicated (i.e. circled or labelled). There must be at least 5 points left after the anomalous point is disregarded. 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 on answer line must match graph. 1 y-intercept: Correct read-off from a point on the line 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 tan θ = 0, accurate to half a small square. 1 Question Answer Marks 1(e) Value of N = candidate’s gradient and value of M = candidate’s intercept. The values must not be fractions. 1 Units for N and M correct (e.g. m or cm or mm). 1

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2 In this experiment, you will investigate the friction between string and a pulley. (a) (i) You have been provided with two lengths of string. Measure and record the diameter d of the thicker string. d = ....................................................mm [2] (ii) Estimate the percentage uncertainty in your value of d. percentage uncertainty = ...........................................................[1] (iii) Calculate the cross-sectional area A of the string using πd 2 A = . 4 A = ...........................................................[1] (iv) Justify the number of significant figures that you have given for your value of A. ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[1] (b) (i) You have been provided with two mass hangers and a pulley. Rotate the pulley to ensure that it rotates freely. • Using the thicker string, set up the apparatus as shown in Fig. 2.1. • pulley boss string stand mass hangers bench Fig. 2.1 Add paper clips to one of the mass hangers until the mass hangers start to move. • Record the number p of paper clips added to the mass hanger. • p = ...........................................................[1] (ii) Remove the paper clips from the mass hanger. • Add paper clips to the other mass hanger until the mass hangers start to move. • Record the number q of paper clips added to the mass hanger. • q = ............................................................... + (p q) Calculate . • 2 + (p q) = ............................................................... 2 [1] (c) Using the thinner string, repeat (a)(i), (a)(iii) and (b). d = ........................................................ mm A = ............................................................... p = ............................................................... q = ............................................................... + (p q) = ............................................................... 2 [3]

Mark scheme: 2(a)(i) 1 Evidence of repeats. 1 2(a)(ii) Absolute uncertainty in d in the range 0.02–0.2 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(a)(iii) Correct calculation of A with correct unit. 1 2(a)(iv) Justification for significant figures in A linked to significant figures in d. 1 2(b)(i) Value of p. 1 2(b)(ii) Correct calculation of (p + q) / 2. 1 2(c) Second value of d. 1 Second values of p and q. 1 Quality: Second value of (p + q) / 2 less than first value of (p + q) / 2. 1 2(d)(i) Two values of k calculated correctly. 1 2(d)(ii) Valid comment consistent with the calculated values of k, testing against a criterion stated by the candidate. 1 Question Answer Marks 2(e)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficulty with measuring d with a reason e.g. string is soft/string is compressed (by micrometer)/diameter not uniform along length. C Difficulty linked to placing paper clips on hanger with a reason e.g. clips slide off/added force from hand/dropping clips starts movement/difficult not to touch hanger when releasing clips/hanger too small for clips. D Idea of increments being too large e.g. large increments of mass (large uncertainty in the value of p or q) or only a small number of clips are added or exact force needed to cause movement may not equal a whole number of clips or mass of each paper clip is too large E Mass of clips may be different or two strings are of different material 1 mark for each point up to a maximum of 4. 4 2(e)(ii) A Take more readings (for different values of d) and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Workable improved method e.g. wrap string round a rod and measure many d/use travelling microscope. C Workable method of adding or holding paper clips e.g. add a hook to each mass hanger/use a wider mass hanger or tweezers. D Improved method of loading e.g. use smaller clips/lighter clips/smaller masses to add to mass hanger or use of sand/water with detail. E Method to check clips have the same mass e.g. use a balance. 1 mark for each point up to a maximum of 4. 4

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