Cambridge A Level Physics 9702 — 2022 Oct/Nov Paper 3 · Variant 6

1 In this experiment, you will investigate the oscillations of a pendulum. (a) (i) ● Assemble the apparatus as shown in Fig. 1.1 with the top nail held securely in the cork by the clamp. Check that the rod can swing freely. cork stand boss top nail clamp rod upper nails lower nails bench Fig. 1.1 ● Slot masses onto the upper and lower nails as shown in Fig. 1.2. nails slotted mass Fig. 1.2 ● Load all of the masses onto the nails in the positions shown in Fig. 1.3. 100 g mass 50 g mass upper nails lower nails Fig. 1.3 ● Record the total mass ML on the four lower nails. ML = ......................................................... [1] (ii) ● Push the bottom of the rod through a short distance and release it so that it oscillates. ● Take measurements to determine the period T of these oscillations. T = ......................................................... [2] (b) Rearrange the slotted masses between the upper and lower nails. Record ML and determine T. Repeat until you have six sets of values. Use all of the slotted masses each time so that the mass of the pendulum is constant. Record your results in a table. Include values of ML to three significant figures in your table. [9] (c) (i) Plot a graph of T on the y‑axis against ML 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] (d) It is suggested that the quantities T and ML are related by the equation T = a ML + b 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: Question Answer Marks 1(a)(i) Value of ML, with unit, equal to 200 g. 1 1(a)(ii) Value of T with unit and in range 0.90–1.60 s. 1 Repeats: at least two measurements of at least 5T. 1 1(b) Six sets of readings of ML and T with correct trend and without help from the Supervisor scores 4 marks, five sets scores 3 4 marks, etc. Range: min ML ⩽ 100 g and max ML ⩾ 500 g. 1 Column headings: 1 Each column heading must contain a quantity and a unit where appropriate 1 2 . The presentation of quantity and unit must conform to accepted scientific convention e.g. ML / g Consistency: 1 All values of raw time must be given to the nearest 0.01 s or all to the nearest 0.1 s. Significant figures: 1 Values of ML given to 3 significant figures. Calculation: 1 Values of ML calculated correctly. 1(c)(i) Axes: 1 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 must be no more than 2 cm (one large square) apart. 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 All points in the table must be plotted (at least 5) for this mark to be awarded. General trend of points must be positive. 1 Scatter of plotted points must be no more than ± 1 g 2 from a straight line in the x ( ML ) direction. 1 1 2 then tolerance is ± 0.03 kg 2 . If ML has unit kg 1(c)(ii) Line of best fit: 1 ‘Best fit’ is judged by the balance of all points on the grid (at least 5) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Candidates do not need to identify an anomalous point. However if there is a point off trend, it may be identified as anomalous by circling or labelling it. There must be at least 5 points left after one anomalous point is disregarded. Lines must not be kinked or thicker than half a small square. 1(c)(iii) Gradient: 1 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 (not x / y). Gradient sign on answer line matches graph drawn. y-intercept: 1 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 x = 0, accurate to half a small square. 1(d) Value of a = candidate’s gradient and b = candidate’s intercept. 1 Values must not be written as fractions. − 21 1 Units for a and b correct and consistent with value (e.g. s g for a and s for b).

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2 In this experiment, you will investigate the optical properties of a transparent block. (a) You are provided with a semicircular transparent block. Take measurements to determine the radius of curvature R of the curved surface, as shown in Fig. 2.1. R Fig. 2.1 R = ......................................................... [1] (b) (i) You are provided with a piece of paper labelled P with four parallel lines drawn on it. ● A is the distance between the two central lines and B is the distance between the two outer lines. Measure and record A and B. A = ............................................................... B = ............................................................... ● Calculate E using B E = A. E = ............................................................... [1] (ii) ● Arrange the apparatus as shown in Fig. 2.2. observer block paper P bench Fig. 2.2 ● Look down through the block and close one eye. The appearance of the lines should be similar to Fig. 2.3. block Fig. 2.3 ● Gradually raise the block until the two central lines seen through the block are aligned with the two outer lines seen outside the block, as shown in Fig. 2.4. You may have to move your head sideways to see this alignment. Fig. 2.4 ● With the block in this position, measure and record the height d1 of the block above the paper, as shown in Fig. 2.5. d1 Fig. 2.5 d1 = .................................................... cm [2] (iii) Estimate the percentage uncertainty in your value of d1. Show your working. percentage uncertainty = ......................................................% [1]

Mark scheme: 2(a) Value of R to nearest mm, with unit, in range 3.5–6.0 cm. 1 2(b)(i) Correct calculation of E with no unit. 1 2(b)(ii) Raw value(s) for d1 to nearest mm. 1 Evidence of repeated readings of d1. 1 2(b)(iii) Absolute uncertainty in range 2–8 mm. 1 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. 2(b)(iv) Value for d2 greater than d1. 1 2(c) Second values of A and B. 1 Second values of d1 and d2. 1 Second d1  first d1 and second d2  first d2. 1 2(d) Two values of k calculated correctly. 1 2(e) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 5% leading to a consistent conclusion. 2(f) Correct calculation of f. 1 2(g)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B Difficulty in measuring distance between central lines (or A) with reason, e.g. large % uncertainty in A / A is small so uncertainty is large. C Difficult to achieve/judge alignment of lines. D Hard to keep block still in correct position. E Difficult to measure d1 (or d2) with reason, e.g. difficult to hold rule still/rule too long/parallax error. F Difficulty in measuring d2 with reason, e.g. judging lowest point of block. 1 mark for each point up to a maximum of 4. 2(g)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). 4 B Measure line spacing using calipers. C Use thinner ruled lines. D Detail of support method for block, e.g. stand and clamp, support on two adjustable stands or perform the experiment sideways so the paper is against the wall and the block lies on the bench. E Improved instrument to measure d1 (or d2), e.g. shorter ruler/clamped ruler/set square instead of ruler/thinner ruler. F Measure to (flat) top of block and subtract radius (for d2). 1 mark for each point up to a maximum of 4.

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