Cambridge A Level Physics 9702 — 2024 May/June Paper 3 · Variant 2

1 In this experiment, you will investigate an electrical circuit. (a) ● Connect the circuit shown in Fig. 1.1. 12 V d.c. S + + + C V R Fig. 1.1 ● Ensure that the polarities of the power supply, component C and the voltmeter are as shown in Fig. 1.1. ● Close switch S for a short time and then open it. ● Watch the voltmeter reading as it reduces. When the voltmeter reading passes a value VS of 8.00 V, start the stop-watch. When the voltmeter reading passes a value of 7.00 V, stop the stop-watch. ● Record the starting value VS and the time T for the voltmeter reading to fall by 1.00 V. VS = ............................................................... T = ............................................................... [2] (b) Choose another starting value VS. Close S for a short time and then open it. Measure the time T for the voltmeter reading to fall by 1.00 V from the starting value VS. Repeat until you have six sets of values of VS and T. 1 Record your results in a table. Include values of in your table. T [10] 1(c) (i) Plot a graph of on the y-axis against VS on the x-axis. [3] T (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 VS and T are related by the equation 1 = aVS + b T where a and b are constants. Using your answers in (c)(iii), 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) Value of T in range 5.00–8.00 s with unit. 1 Evidence of repeat measurements of T. 1 1(b) Six sets of readings of VS (different values) and T with correct trend (average T increases as VS decreases) and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: VS (min) ⩽ 4.00 V and VS (max) ⩾ 10.00 V. 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 / T / s–1. 1 Consistency: All values of T must be given to the nearest 0.01 s (or all to the nearest 0.1 s). 1 Significant figures: Values of 1 / T given to same number of s.f. as (or one more than) the number of s.f. in T. 1 Calculation: Values of 1 / T calculated correctly 1 1(c)(i) Axes: Axes must be labelled with the required quantities. Scales must be chosen so that the plotted points occupy at least half the graph grid in both the x and y directions. Scale markings are no more than 2 cm (one large square) apart. Sensible scales must be used. Scales must not be awkward (e.g. 3:10 or fractions). 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 the x and y directions. 1 Quality: All points in the table (at least 5) must be plotted on the grid. Trend must be correct. It must be possible to draw a straight line that is within  0.40 V on the Vs axis of all plotted points. 1 Question Answer Marks 1(c)(ii) Line of best fit: ‘Best fit’ is judged by balance of all points on the grid (at least 5 points) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Lines must not be kinked or thicker than half a small square. Some candidates may choose to identify an anomalous point. If they identify one point as anomalous (e.g. by circling or labelling) then this point is to be disregarded when judging the line of best fit. There must be at least 5 points left after the anomalous point is disregarded. 1 1(c)(iii) Gradient: The hypotenuse of the triangle used should 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. The method of calculation must be correct, not x / y. The gradient sign on the answer line must be consistent with the graph drawn. 1 y-intercept: Correct read-off from a point on the line and substituted correctly into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both the x and y directions. or Intercept read directly from the graph, with read-off at Vs = 0, accurate to half a small square in y direction. 1 1(d) Value a = candidate’s gradient and value of b = candidate’s intercept. Values must not be written as fractions or given to only one significant figure. 1 Units for a and b correct and consistent with the readings taken (e.g. V–1 s–1 for a and s–1 for b). 1

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2 In this experiment, you will investigate the equilibrium of a wooden rod. (a) (i) ● Assemble the apparatus as shown in Fig. 2.1. ● Adjust the apparatus so that the wooden rod is parallel to the bench and the spring is vertical. clamp nail held in cork stand stand boss wooden rod L0 boss spring clamp bench mass hanger nail through rod and mass and held in cork Fig. 2.1 (not to scale) ● The distance between the ends of the spring is L0, as shown in Fig. 2.1. Measure and record L0. L0 = ...................................................... m [1] (ii) ● Pull the mass hanger down a short distance and then release it. The mass hanger will oscillate. ● Take measurements to find the period T of the oscillations. T = ......................................................... [2] (iii) ● Calculate the value of the spring constant k using α π2 k = T 2 where α = 0.800 kg. k = ..................................................... N m–1 ● Justify the number of significant figures that you have given for your value of k. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... [1] (b) (i) ● Move the stand supporting the spring away from the other stand and add the plumb line, as shown in Fig. 2.2. θ plumb line L Fig. 2.2 (not to scale) ● Adjust the apparatus so that the angle θ between the spring and the vertical is approximately 20° and the wooden rod is parallel to the bench, as shown in Fig. 2.2. ● The new distance between the ends of the spring is L, as shown in Fig. 2.2. Measure and record L. L = ........................................................... m ● Measure and record θ. θ = ............................................................. ° [2] (ii) Estimate the percentage uncertainty in your value of θ. Show your working. percentage uncertainty = ......................................................% [1]

Mark scheme: 2(a)(i) Value for L0 to nearest mm and in range 0.050–0.200 m. 1 2(a)(ii) Value for T with unit. 1 Evidence of repeat readings: at least two measurements each of at least 5T. 1 2(a)(iii) Justification linked to significant figures in time / T (and ). 1 2(b)(i) Value for L greater than L0. 1 Value for  to nearest degree and in range 15°–25°. 1 2(b)(ii) Absolute uncertainty in  in range 2°–5°. Correct method of calculation to obtain percentage uncertainty e.g. (absolute uncertainty / value from (b)(i))  100. If several readings have been taken, then the absolute uncertainty can be half the range (but not zero) provided the working is shown clearly. 1 2(b)(iii) Second value of L. 1 Second value of . 1 Second value of L > first value of L. 1 2(c) Two values of D calculated correctly. The final D values must not be written as fractions or given to only one significant figure. 1 2(d) Calculation of percentage difference between candidate’s two D values. Comparison of percentage difference with 10% leading to a consistent conclusion. 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 measure T with reason, e.g. difficult to judge/determine/decide end or start of a complete oscillation. C Difficult to measure L or L0 with reason, e.g. parallax error / difficult to hold ruler steady next to spring / spring moves when touched by ruler / ruler not parallel to spring. D Difficulty with setting up apparatus e.g. difficult to ensure wooden rod is parallel to bench / difficult to ensure that spring is vertical / stands slide on bench or fall over when setting larger angle. E Difficult to measure  with reason e.g. parallax / difficult to hold protractor steady / strings (or plumb line) move when touched by protractor / thick strings. 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 D values (not “repeat readings” on its own). B Method to improve measurement of T with detail e.g. use marker placed at midpoint/equilibrium point of oscillation or record/film/video with timer or record/film/video and view frame by frame or use a position/distance sensor placed below mass with data logger. C Improved method of measuring L or L0 e.g. calipers/clamp ruler (next to spring). D Measure from rod to bench at both ends / use spirit level beside wooden rod / spirit level beside spring (for L0) / plumb line beside spring (for L0) or method to stop stand sliding e.g. G-clamp (to bench) or add mass to base or use heavier stand(s). E Method to improve measurement of  e.g. hold protractor in clamp / measure using photograph / use thinner string / use of trigonometry with length measurements described. 1 mark for each point up to a maximum of 4. 4

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