Cambridge A Level Physics 9702 — 2023 May/June Paper 3 · Variant 3

1 In this experiment, you will investigate the motion of a pendulum. You have been provided with a cylinder and a pendulum. (a) ● Use adhesive putty to attach the string to the cylinder as shown in Fig. 1.1. L adhesive putty P string bob cylinder Fig. 1.1 ● P is the point at which the string is attached to the cylinder. The distance between P and the centre of the bob is L. Adjust the adhesive putty and string so that L is approximately 45 cm. ● Measure and record L. L = ......................................................... [1] (b) ● Set up the apparatus as shown in Fig. 1.2. clamp cylinder boss stand bob bench Fig. 1.2 ● Move the bob a short distance away from the stand, as shown in Fig. 1.2. ● Release the bob. The bob will oscillate. ● Determine the period T of the oscillations of the bob. T = ......................................................... [2] (c) Change L by attaching a different point on the string to the cylinder and determine T. Repeat until you have six sets of values of L and T. Record your results in a table. Include values of T 3 and L2 in your table. [9] (d) (i) Plot a graph of T 3 on the y-axis against L2 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 T and L are related by the equation T 3 = EL2 + F where E and F are constants. Using your answers in (d)(iii), determine the values of E and F. Give appropriate units. E = ............................................................... F = ............................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of L in the range 40.0–50.0 cm with consistent unit. 1 1(b) Value of T in the range 1.0–1.5 s with unit. 1 Evidence of repeats of nT where n ⩾ 5. 1 1(c) Six sets of readings of L (different values) and time with correct trend (time increases as L increases) and without help from the Supervisor scores 4 marks, five sets scores 3 marks, etc. 4 Range: Lmin ⩽ 30.0 cm and Lmax ⩾ 55.0 cm. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit conforms to scientific convention e.g. T 3 / s3 and L2 / m2. 1 Consistency: All raw values of L given to the nearest millimetre. 1 Significant figures: All values of L2 must be given to the same number of s.f. as (or one more than) the number of significant figures in raw L. 1 Calculation: Correct calculation of L2. 1 Question Answer Marks 1(d)(i) Axes: Axes must be labelled with the correct quantities. Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scale markings are no more than 2 cm apart (one large square). Sensible scales must be used. Scale 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 less than half a small square. Points must be plotted to an accuracy of half a small square in both x and y directions. 1 Quality: Trend of points must be positive. All points in the table must be plotted on the grid. It must be possible to draw a straight line that is within  0.02 m2 (200 cm2) on the L2 axis of all plotted points. 1 1(d)(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 Question Answer Marks 1(d)(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 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: Intercept read directly from the graph, with read-off at L2 = 0, accurate to half a small square in y direction. or Correct read-off from a point on the line and substituted correctly into y = mx + c or an equivalent expression. Read-off is accurate to half a small square in both x and y directions. 1 1(e) Value of E = candidate’s gradient and value of F = candidate’s intercept. The values must not be written as fractions or given to only one significant figure. 1 Units for E consistent with readings: s3 m–2 or s3 cm–2 and units for F: s3. 1

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2 In this experiment, you will investigate the equilibrium of a card. You have been provided with a card. (a) The card has one edge of length h and another edge of length x, as shown in Fig. 2.1. card h x Fig. 2.1 (i) Measure and record h and x. h = ......................................................... cm x = ......................................................... cm [1] (ii) Calculate the area A of the card, where 5x2 A = hx + . 8 A = ...................................................cm2 [1] (iii) Justify the number of significant figures that you have given for your value of A. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (b) (i) ● Use the nail to make a hole close to one corner of the card, as shown in Fig. 2.2. hole Fig. 2.2 ● Set up the apparatus as shown in Fig. 2.3. boss nail stand bench Fig. 2.3 ● Push the nail through the hole in the card. ● Fix the nail in the boss. ● Ensure that the card swings freely from the nail. ● Use the set square and the ruler to draw a vertical line on the card below the nail. ● Repeat using two more holes close to two other corners of the card. ● Fig. 2.4 shows an example of the card with three lines drawn on it. The three lines cross at distances c and d from the two edges of the card shown in Fig. 2.4. line d hole c Fig. 2.4 Measure and record c and d. c = ......................................................... cm d = ......................................................... cm [2] (ii) Estimate the percentage uncertainty in your value of c. Show your working. percentage uncertainty = ..................................................... % [1]

Mark scheme: 2(a)(i) Values of h and x to the nearest mm. 1 2(a)(ii) Correct calculation of A in the range 150–170 cm2. 1 2(a)(iii) Justification for significant figures in A linked to significant figures in x and h. 1 2(b)(i) Values of c and d to the nearest mm. 1 Values of c and d in the range 6.0–8.0 cm. 1 2(b)(ii) Percentage uncertainty in c based on absolute uncertainty in the range 2–8 mm. 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(c)(i) Raw value(s) of x to the nearest mm in the range 8.5–9.5 cm. 1 2(c)(ii) Second value of c. 1 Second value of d. 1 Second values of c and d less than first values of c and d respectively. 1 2(d) Two values of k calculated correctly. The final k values must not be written as a fraction or given to only one significant figure. 1 2(e) Calculation of percentage difference between candidate’s two k values. Comparison of percentage difference with 5% leading to a consistent conclusion. 1 Question Answer Marks 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to draw lines with reason e.g. ruler moving/card moving/nail in the way/no support behind card/card flexible/parallax error/card suspended. C Difficult to judge vertical/get line vertical/get ruler vertical. D Lines did not meet at a point/not unique intersection/triangle of error. E Problem with card e.g. difficult to cut parallel edge/card bends or deforms or tears when nail punches. F Card doesn’t hang or swing freely or friction between card and nail. 1 mark for each point up to a maximum of 4. 4 2(f)(ii) A Take more readings (for different values of x) and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Clamp ruler or mark card and then remove and draw line with card on the bench. C Use plumb-line or spirit level. D Use more holes/lines (to locate the point more accurately) or use thinner nail/needle/pin/smaller holes. E Use a hole punch or use support beneath when punching nail or use a guillotine/template/paper trimmer/rotary cutter /paper cutter or score with a (sharp) knife along (metal) ruler. 1 mark for each point up to a maximum of 4. 4

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