Cambridge A Level Physics 9702 — 2023 Oct/Nov Paper 3 · Variant 3

1 In this experiment, you will investigate the oscillations of a pendulum. (a) ● Set up the apparatus as shown in Fig. 1.1. clamp wooden blocks boss stand L string sphere of adhesive putty bench Fig. 1.1 ● The length L of the pendulum is the distance between the bottom of the wooden blocks and the centre of the adhesive putty. Adjust the length of the string so that L is approximately 53 cm. ● Measure and record L. L = ................................................... cm [1] (b) ● Use the second boss to attach the wooden rod to the stand. Adjust the apparatus until the vertical string of the pendulum just touches against the wooden rod, as shown in Fig. 1.2. S boss wooden rod Fig. 1.2 ● The distance between the bottom of the wooden blocks and the centre of the wooden rod is S. Adjust the position of the wooden rod so that S is approximately 36 cm. ● Measure and record S. S = ......................................................... cm ● Calculate (L – S). (L – S) = ......................................................... cm ● Move the adhesive putty a small distance so that the string moves away from the wooden rod. Release the adhesive putty. The string hits the rod as the pendulum oscillates. ● Take measurements to determine the period T of the oscillations. T = ............................................................ s [2] (c) Change S in the range 5.0 cm G S G 45.0 cm by adjusting the position of the wooden rod. Determine T. Repeat until you have six sets of values of S and T. Record your results in a table. Include values of (L - S ) in your table. [8] (d) (i) Plot a graph of T on the y-axis against (L - S ) 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) (i) It is suggested that the quantities T, L and S are related by the equation T = A (L - S) + B where A and B are constants. Using your answers in (d)(iii), determine the values of A and B. Give appropriate units. A = ............................................................... B = ............................................................... [2] (ii) Theory suggests that A = π g where g is the acceleration of free fall. Use your answer in (e)(i) to determine a value for g. Give an appropriate unit. g = ......................................................... [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: Question Answer Marks 1(a) Value of L in range 52.5–53.5 cm. 1 1(b) Value of T in the range 1.00–2.00 s. 1 At least two measurements of nT where n ⩾ 5. 1 1(c) Six (or more) sets of readings of S (different values) and T with the correct trend (as S increases T decreases) and without 4 help from the Supervisor scores 4 marks, five sets scores 3 marks, etc. Range: Includes S ⩽ 10.0 cm and S ⩾ 40.0 cm. 1 Column headings: 1 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. √(L – S) / cm1/2. Consistency: All values of S must be given to the nearest 0.1 cm. 1 Calculation: Values of √(L – S) are correct. 1 1(d)(i) Axes: 1 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 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). Plotting of points: 1 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. Quality: 1 Trend of points must be positive. All points in the table must be plotted on the grid (at least 5). It must be possible to draw a straight line that is within  0.2 cm1/2 ( 0.02 m1/2) on the √(L – S) axis of all plotted points. 1(d)(ii) Line of best fit: 1 ‘Best fit’ is judged by the 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 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(d)(iii) Gradient: 1 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. y-intercept: 1 Intercept read directly from the graph, with read-off at x = 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 accurate to half a small square in both x and y directions. 1(e)(i) Value of A = candidate’s gradient and value of B = candidate’s y-intercept. 1 The values must not be written as fractions or surds or given to only one significant figure. Unit for A: s m–1/2 or s cm–1/2 1 and unit for B: s. 1(e)(ii) g calculated correctly using g = 2 / A2 and with correct unit. 1

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2 In this experiment, you will investigate a wooden strip resting at an angle. (a) (i) ● You are provided with a wooden strip, as shown in Fig. 2.1. x y z Fig. 2.1 (not to scale) The dimensions of the strip are x, y and z. Measure and record x, y and z. x = ........................................................... m y = ........................................................... m z = ........................................................... m ● The volume V of the strip is given by the equation V = xyz. Calculate V. V = ......................................................... m3 [2] (ii) Justify the number of significant figures that you have given for your value of V. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (b) (i) ● Set up the apparatus as shown in Fig. 2.2. stand rod of clamp R 1 cm boss wooden strip ≈ 5 cm ≈ 0.30 m 30 cm ruler secured by adhesive putty bench Fig. 2.2 (not to scale) ● Adjust the position of the boss so that the rod of the clamp is approximately 0.30 m above the bench. ● Use some of the adhesive putty to secure the 30 cm ruler to the bench, as shown in Fig. 2.2. ● The raised end of the wooden strip is R, as shown in Fig. 2.2. Place the wooden strip on the rod and adjust the position of the stand so that the distance between the rod and R is approximately 5 cm. ● Use adhesive putty to attach the mass to the wooden strip so that the distance d between the lower end of the wooden strip and the centre of the mass is approximately 0.15 m, as shown in Fig. 2.3. mass d ≈ 0.15 m adhesive ruler putty Fig. 2.3 ● Measure and record d. d = ..................................................... m [1] (ii) ● Use adhesive putty to attach the loop of string at the raised end R of the wooden strip, as shown in Fig. 2.4. newton meter loop adhesive putty d Fig. 2.4 ● Use the newton meter to determine the vertical force F needed to just lift the wooden strip from the rod. F = ..................................................... N [2] (iii) Estimate the percentage uncertainty in your value of F. Show your working. percentage uncertainty = ..................................................... % [1]

Mark scheme: 2(a)(i) x, y and z measured to the nearest millimetre and x in the range 0.495–0.505 m. 1 Correct calculation of volume. 1 2(a)(ii) Justification for significant figures in V linked to significant figures in x, y and z. 1 2(b)(i) d in the range 0.145–0.155 m. 1 2(b)(ii) F measured to the nearest 0.01 N and final F in range 0.10–1.00 N. 1 At least two measurements of F. 1 2(b)(iii) Percentage uncertainty in F based on an absolute uncertainty in the range 0.02–0.06 N. 1 Correct method of calculation to obtain percentage uncertainty, e.g. (absolute uncertainty  100 / final value from (b)(ii)). If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is shown clearly. 2(b)(iv) Second value of d and second value of F. 1 Second value of F larger than first value of F. 1 2(c) Two values of k calculated correctly. 1 The final k values must not be written as fractions or given to only one significant figure. 2(d) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 15% leading to a consistent conclusion. 2(e) Correct calculation of with correct unit e.g. kg m–3. 1 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B y is small so uncertainty is large or large percentage uncertainty in measuring y. C Difficult to measure d with a reason e.g. difficult to judge the centre of the mass, parallax error, difficult to hold/maintain ruler parallel to strip. D Difficult to get a value of F with reason e.g. reading changes suddenly or difficult to determine when strip leaves the rod. E Difficult to keep/ensure/maintain the newton meter vertical. F Newton meter not at the end of the strip. G Mass of adhesive putty not taken into account. 1 mark for each point up to a maximum of 4. 2(f)(ii) A Take more readings (for different values of d) and plot a graph or take more readings and compare k values (not 4 “repeat readings” on its own). B Improved method to measure y e.g. use micrometer or (vernier/digital) calipers. C Improved method to measure d e.g. measure to the edge of the mass and add on the radius of the mass or clamp ruler. D Improved method to get value F e.g. video/record/film with newton meter (and strip) in view or force sensor and data logger. E Improved method to ensure vertical e.g. use a clamped metre rule and a set square to ensure vertical or use a plumb line as reference. F Add a hook/tape at end or tape string to strip or glue string to strip. G Subtract weight of putty from F or add mass of putty onto the mass or tape mass (instead of putty). 1 mark for each point up to a maximum of 4.

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