Cambridge A Level Physics 9702 — 2021 May/June Paper 3 · Variant 2

1 In this experiment, you will investigate the patterns produced by overlaid grids. (a) Grid A is the grid of parallel, equally spaced lines shown in Fig. 1.1. grid A Fig. 1.1 Take measurements to determine the average spacing sA between the centres of the lines on grid A. sA = ...................................................mm [2] (b) You have been provided with a second grid (labelled grid B) printed on a transparent sheet. ● Place grid B on top of grid A in Fig. 1.1. ● Turn grid B so that there is a small angle G between the grids. A pattern of fringes will be produced, as shown in the example in Fig. 1.2. F fringes grid A grid B G Fig. 1.2 ● Do not take measurements from Fig. 1.2. Measure and record your value of G from Fig. 1.1. G = ............................................................ ° ● The fringes make an angle F with grid A, as shown in Fig. 1.2. Measure and record your value of F from Fig. 1.1. F = ............................................................ ° [1] (c) Rotate grid B and repeat (b) until you have six sets of values of G and F. Use values of G in the range 0° to 20°. Record your results in a table. Include values of sin F and sin (F – G) in your table. [8] (d) (i) Plot a graph of sin (F – G) on the y-axis against sin F 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 F and G are related by the equation sin (F – G) = p sin F + q where p and q are constants. Use your answers in (d)(iii) to determine the values of p and q. p = ............................................................... q = ............................................................... [2] (f) The constant p is related to the spacing of the lines of grids A and B by sB p = sA where sB is the line spacing of grid B. Use your values of p and sA to calculate sB. sB = ...................................................mm [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Final value of sA to at least two significant figures and in the range 1.05–1.10 mm. 1 Evidence that sA has been correctly calculated from a measurement of at least 10sA. 1 1(b) Value of G in range 0°–45°. 1 1(c) Six (or more) sets of readings of G and F (different values) with correct trend (F increases as G increases) and without help from the Supervisor scores 3 marks, five sets scores 2 marks, four or fewer sets scores 1 mark. 3 Range: Gmin ⩽ 3° and Gmax ⩾ 17°. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. Headings for sin F and sin (F–G) must have no unit. The presentation of quantity and unit must conform to accepted scientific convention e.g. F / °. 1 Consistency: All values of raw G and raw F must be given to the nearest degree. 1 Significant figures: Values of sin F should be to the same number of significant figures as, or one greater than, the number of significant figures in the corresponding value(s) of raw F. 1 Calculation: Values of sin (F–G) 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 are chosen so that the plotted points occupy at least half the graph grid in both x and y directions Axes 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 are ⩽ half a small square. Points must be plotted to an accuracy of half a small square. 1 Quality: All points in the table must be plotted (at least 5) on the grid. Trend of points on graph must be correct. It must be possible to draw a straight line that is within ± 0.02 on the sin F 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 by the candidate. There must be at least five 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. Method of calculation must be correct, i.e. Δy / Δx. Gradient sign on answer line matches graph drawn. Both read-offs must be accurate to half a small square in both the x and y directions. 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 at x = 0, accurate to half a small square. 1 Question Answer Marks 1(e) Value of p equal to candidate’s gradient and value of q equal to candidate’s intercept. Values must not be written as fractions. 1 Values for p and q both given without a unit. 1 1(f) Correct calculation of sB using sB = psA. 1

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2 In this experiment, you will investigate the oscillations of a mass on a spring. (a) (i) ● Set up the apparatus as shown in Fig. 2.1 using the 50 g mass hanger. stand boss rod of clamp spring ≈ 50 cm 50 g mass hanger bench Fig. 2.1 ● Pull the mass hanger down by approximately 1 cm. Release it so that it oscillates vertically, with no swinging motion. ● Take measurements to find the period TV of these oscillations. TV = ......................................................... [2] (ii) ● Ensure that the mass hanger has stopped moving. ● Push the mass hanger approximately 1 cm away from you. Release it so that it swings towards and away from you, with as little vertical oscillation as possible. ● Take measurements to find the period TS of these oscillations. TS = ......................................................... [1] (b) Repeat (a) with a total mass of 150 g suspended from the spring. TV = ............................................................... TS = ............................................................... [2] (c) It is suggested that the quantity TS2 – TV2 is independent of the mass suspended from the spring. (i) Using your data, calculate two values of TS2 – TV2. first value of TS 2 – TV 2 = ............................................................... second value of TS 2 – TV 2 = ............................................................... [1] (ii) Justify the number of significant figures you have given for your values of TS2 – TV2. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (iii) Explain whether your results in (c)(i) support the suggestion. ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1]

Mark scheme: 2(a)(i) Value of TV with unit and in range 0.20–0.40 s. 1 At least two measurements of nTV where n ⩾ 5. 1 2(a)(ii) Value for TS larger than TV. 1 2(b) Second values of TV and TS. 1 Second TS > first TS. 1 2(c)(i) Two values of TS2 – TV2 calculated correctly. 1 2(c)(ii) Justification based on significant figures in TS and TV. 1 2(c)(iii) Valid comment consistent with the calculated values of TS2 – TV2, testing against a criterion stated by the candidate. 1 2(d)(i) Value for x1 in range 4.0–6.0 cm. 1 2(d)(ii) Percentage uncertainty based on an absolute uncertainty in the range 2–3 mm. If repeat readings have been taken, then the absolute 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)(iii) Raw value(s) for x2 to nearest 0.1 cm. 1 2(d)(iv) Correct calculation of g with consistent unit. 1 Question Answer Marks 2(e)(i) A Two TS2 – TV2 values are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to maintain single mode of oscillation e.g. spring swings when measuring vertical oscillations/spring bounces when measuring swinging oscillations/spring swings in more than one plane. C Spring slides along rod during the oscillation. D Difficult to judge/determine/decide when an oscillation starts/ends/is complete. E Large % uncertainty in Tv or Tv is small so large uncertainty. F Difficult to measure x1 or x2 with reason e.g. parallax error or difficult to measure x2 due to space at end of ruler. 1 mark for each point up to a maximum of 4. 4 2(e)(ii) A Take more readings and plot a graph or take more readings and compare (not “repeat readings” on its own). B Method to help maintain single mode of oscillation e.g. restrict sideways motion with tube/use parallel guides. C Method to attach spring to rod/stop spring sliding on rod e.g. adhesive putty/glue spring to rod/cut notch in rod/use rod with diameter same as diameter of spring loop/rougher rod. D Video/record/film with timer in view/frame by frame or use fiducial marker at centre of oscillation. E Use larger masses/use spring with lower spring constant/stiffness. F Use calipers/travelling microscope/use ruler starting at zero/use blocks with detail. 1 mark for each point up to a maximum of 4. 4

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