Cambridge A Level Physics 9702 — 2021 Oct/Nov Paper 3 · Variant 4

1 In this experiment you will investigate an electrical circuit. (a) (i) ● Assemble the circuit shown in Fig. 1.1. 3 V d.c. M N V wooden strip wire 1 A B p E C D wire 2 q wooden strip Fig. 1.1 ● A, B, C and D are crocodile clips. Connect A approximately half-way along wire 1. ● Measure and record the distance p between B and A, as shown in Fig. 1.1. p = ......................................................... cm ● Close the switch. ● Test your circuit by placing C at end E of wire 2. The voltmeter reading should be non-zero. Record the voltmeter reading. voltmeter reading = ........................................................... V ● Open the switch. [1] (ii) ● Close the switch. ● Adjust the position of C on wire 2 until the voltmeter reading is as close as possible to zero. ● The distance between C and E is q, as shown in Fig. 1.1. Measure and record q. q = ......................................................... cm ● Open the switch. [1] (b) Move A to a new position on wire 1. Measure and record p and repeat (a)(ii). Repeat until you have six sets of values for p and q. 1 p Record your results in a table. Include values of and in your table. q q [10] 1 p(c) (i) Plot a graph of on the y-axis against on the x-axis. [3] q q (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 p and q are related by the equation 1 p = a + b q ( q) 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 p in range 35.0–45.0 cm. 1 1(a)(ii) Value of q in range 50.0–70.0 cm 1 1(b) Six sets of readings of p and q (different values) with correct trend and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: pmin ⩽ 25.0 cm and pmax ⩾ 65.0 cm. 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 / q (cm–1). p / q must have no unit. 1 Consistency: All values of q and p must be given to the nearest mm. 1 Significant figures: All values of 1 / q should have the same number of s.f. as, or one more than, the number of s.f. in the corresponding raw q value(s). 1 Calculation: Values of 1 / q calculated correctly 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 the 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 must be ⩽ half a small square. Points must be plotted to an accuracy of half a small square in both x and y directions. 1 Quality: All points in the table (at least 5) must be plotted on the grid. Trend of points must be correct. It must be possible to draw a straight line that is within ± 0.001 cm–1 (± 0.1 m–1) on the 1 / q axis (normally y-axis) of all plotted points. 1 1(c)(ii) Line of best fit: Judge by the 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) by the candidate. There must be at least five points left after the anomalous point is disregarded. Line 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. Both read-offs must be accurate to half a small square in both the x and y directions. Method of calculation must be correct, e.g. Δy / Δx. Gradient sign on answer line matches graph drawn. 1 y-intercept: Correct read-off from a point on the line and substituted into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at p / q = 0, accurate to half a small square. 1 Question Answer Marks 1(d) Value of a equal to candidate’s gradient and value of b equal to candidate’s intercept. Values are not written as fractions. 1 Units for a and b correct (e.g. cm–1). 1

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2 In this experiment, you will investigate the oscillations of a suspended rod. (a) (i) ● You are provided with a pin pushed into a cork. Clamp the cork to the stand so that the pin is horizontal and approximately 50 cm above the bench. ● You are provided with a rod with two strings attached. The distance between the two holes in the rod is y, as shown in Fig. 2.1. y hole rod string Fig. 2.1 Measure and record y. y = ................................................... cm [1] (ii) ● Set up the apparatus as shown in Fig. 2.2. ● Tie the two strings together so that, when the rod is suspended from the pin, the top of the rod is approximately 30 cm below the pin. stand pin boss cork clamp string ≈ 30 cm rod θ bench Fig. 2.2 ● Ensure that the rod is horizontal. ● The angle between the rod and the string is θ, as shown in Fig. 2.2. Measure and record θ. θ = ........................................................° [1] (iii) Estimate the percentage uncertainty in your value of θ. Show your working. percentage uncertainty = ......................................................... [1] (iv) Calculate D where y tan θ D = . 2 D = ......................................................... [1] (v) Justify the number of significant figures that you have given for your value of D. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (b) (i) ● Push the rod approximately 2 cm to one side and then release it so that it swings as shown in Fig. 2.3. Fig. 2.3 ● Take measurements to determine the period S of these oscillations. S = ......................................................... [2] (ii) ● Return the rod to a horizontal and stationary position. ● Push the whole rod approximately 2 cm away from you and release it so that it swings towards and away from you. As it swings, the rod should always remain parallel to its stationary position with no twisting or sideways motion. ● Take measurements to determine the period B of these oscillations. B = ......................................................... [1]

Mark scheme: 2(a)(i) Raw value(s) of y to nearest 0.1 cm and final value in range 44.0–48.0 cm. 1 2(a)(ii) Raw value(s) of θ to nearest degree and final value in range 40–60°. 1 2(a)(iii) Percentage uncertainty based on an absolute uncertainty in the range 2–5°. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if working is clearly shown. Correct method of calculation to find percentage uncertainty. 1 2(a)(iv) Correct calculation of D. 1 2(a)(v) Justification based on significant figures in y and θ. 1 2(b)(i) Final value of S with unit and in range 1.00–1.50 s. 1 Repeats: at least two values of nS, where n ⩾ 5. 1 2(b)(ii) All raw times to nearest 0.1 s or all to nearest 0.01 s. 1 2(c) Second values for θ, S and B. 1 Quality: B decreases as θ decreases. 1 2(d)(i) Two values of k calculated correctly. The final k values must not be written as fractions. 1 2(d)(ii) Valid comment relating to 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 Difficult to set or keep rod horizontal or string slips on pin. C Difficult to measure θ with reason e.g. rod moves if touched/parallax error/difficult to hold protractor steady in hand. D Difficulty with mode of oscillation e.g. rod oscillates in more than one plane/different modes of oscillation/rod twists as it oscillates from side to side. E Difficulty with B oscillation with reason e.g. rod hits stand/difficult to release both ends at the same time/hands get in the way at release. F Difficult to judge/determine/tell/know start of/end of/complete oscillation. 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 k values (not “repeat readings” on its own). B Notch in pin/use rough pin. C Clamp protractor/take a photograph and measure θ on photo/measure lengths and use trigonometry. D Method of restricting other modes of oscillation e.g. two sheets placed either side of rod. E Improved method of release for B oscillation, e.g. pull towards you/use card gate to release both ends at the same time or use longer pin. F Video/film/record with timer in view/view frame-by-frame or use (fiducial) marker at midpoint of oscillation. 1 mark for each point up to a maximum of 4. 4

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