Cambridge A Level Physics 9702 — 2017 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate the motion of a pendulum. (a) Assemble the apparatus as shown in Fig. 1.1 with the total mass m of the mass hanger and mass equal to 150 g. The distance between the bottom of the split cork and the bottom of the mass hanger should be 64 cm. It may be necessary for the mass to hang over the edge of the bench. clamp boss split cork string knot 64 cm spring mass hanger mass G-clamp bench Fig. 1.1 (b) (i) Move the mass a short distance to one side and then carefully release it so that it swings with as little bouncing as possible, as shown in Fig. 1.2. Fig. 1.2 (ii) Take measurements to determine the period T of the pendulum. T = ................................................. [2] (c) Change m and repeat (b) until you have six sets of values of m and T. Do not adjust the string in the split cork. Record your results in a table. Include values of T 2 in your table. [10] (d) (i) Plot a graph of T 2 on the y-axis against m 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 m are related by the equation T 2 = a m + b where a and b are constants. Use your answers from (d)(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(b)(ii) Value of T with unit in range 1.00–2.00 s. 1 Evidence of repeated readings of nT. 1 1(c) Six sets of readings of m (different values) and T with correct trend and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: mmin = 50 g and mmax ⩾ 350 g. 1 Column headings: Each column heading must contain a quantity and a unit. The presentation of quantity and unit must conform to accepted scientific convention e.g. T2 / s2. 1 Consistency: All values of time must be given to the nearest 0.1 s or all values to the nearest 0.01 s. 1 Significant figures: Significant figures of every value of T 2 must be the same as, or one greater than, the s.f. of the raw times as recorded in table. If raw times recorded to nearest 0.01 s, allow number of significant figures of T2 to be one less than the number of significant figures of the raw times. 1 Values of T2 calculated correctly. 1 Question Answer Marks 1(d)(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 x and y directions. Scales 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 must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square (no “blobs”). Points must be accurate to within half a small square in both x and y directions. 1 Quality: All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of points must be no more than ±25 g from a straight line in the m direction (x-axis). 1 1(d)(ii) Line of best fit: Judge by 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. Allow one anomalous point only if clearly indicated (i.e. circled or labelled) by the candidate. Lines must not be kinked or thicker than half a small square. 1 1(d)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. The method of calculation must be correct. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression. Read-off must be accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off accurate to half a small square in the y direction. 1 1(e) Value of a = candidate’s gradient and value of b = candidate’s intercept. The values must not be fractions. 1 Correct units for a (e.g. s2 g–1) and b (s2). 1

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2 In this experiment, you will investigate an optical system. (a) (i) Use a small piece of Plasticine to fix the torch horizontally on one of the wooden blocks. (ii) Put the remaining Plasticine inside the transparent container and push the lens into it so that the lens is held vertically and parallel to two opposite sides of the container. (b) (i) Position the apparatus as shown in Fig. 2.1, with the front of the torch approximately 32 cm from the lens. torch with transparent bright LEDs container lens ≈ 32 cm Plasticine wooden blocks bench Fig. 2.1 (not to scale) (ii) Switch on the torch. (iii) Measure the distance u from the front of the torch to the centre of the lens, as shown in Fig. 2.2. u = ................................................. [1] (iv) Place the white screen as shown in Fig. 2.2. Keeping the screen vertical, move it until it shows a sharp image of the LEDs in the torch. (v) Measure the distance v from the centre of the lens to the screen, as shown in Fig. 2.2. v = ................................................. [1] u v sharp image § 32 cm here white screen bench Fig. 2.2 (not to scale) (c) Estimate the percentage uncertainty in your value of v. percentage uncertainty = ................................................. [1] uv(d) Calculate the value of f using the expression f = . (u + v) f = ................................................. [1] (e) (i) Without moving the container and the torch, pour water into the container to submerge the lens. (ii) Reposition the screen so that it shows a sharp image of the LEDs. (iii) Measure the new distance vw from the lens to the screen. vw = ................................................. [2] uvw (iv) Calculate fw using fw = . (u + vw) fw = ...................................................... (v) Switch off the torch. (f) Justify the number of significant figures you have given for your value of fw. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[1] (g) (i) Pour the water from the container back into the beaker, making sure that the lens remains fixed in the container. (ii) Repeat (b), (d) and (e) but with the front of the torch approximately 22 cm from the lens. u = ...................................................... v = ...................................................... f = ...................................................... vw = ...................................................... fw = ...................................................... [3]

Mark scheme: 2(b)(iii) Value of u with unit in range 30.0–34.0 cm. 1 2(b)(v) (Raw) value(s) of v to nearest 0.1 cm. 1 2(c) Absolute uncertainty in v in range 0.2–0.8 cm and correct method of calculation to obtain percentage uncertainty. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. 1 2(d) Correct calculation of f. 1 2(e)(iii) Value of vw. 1 Quality: vw > v. 1 2(f) Justification for s.f. in fw linked to s.f. in u and vw. 1 2(g)(ii) Second value of u in range 20.0–24.0 cm. 1 Second value of v. 1 Quality: second value of vw > first value of vw. 1 2(h)(i) Two values of k calculated correctly. 1 2(h)(ii) Valid comment consistent with calculated values of k, testing against a criterion stated by the candidate. 1 Question Answer Marks 2(i)(i) A Two readings/too few readings/only two readings not enough to draw a (valid) conclusion. B Difficult to judge/obtain sharp image/hard to focus. C Difficult to keep screen steady/vertical (to measure v) or difficult to hold screen and measure distance (at the same time). D Difficult to measure u (or v) with reason e.g. parallax error/judging front of torch/judging centre of lens. E LEDs not at the front of torch/u should be measured to the LEDs. F Difficult to align torch, lens and screen or torch and lens at different heights or lens not vertical. 1 mark for each point up to a maximum of 4. 4 2(i)(ii) A Take more readings and plot a graph/calculate more k values and compare. B Use dark(ened) room/turn off lights or use improved ‘object’ e.g. cross-hairs/filament lamp/smaller LEDs. C Mount screen in holder/clamp screen or clamp ruler/fix ruler to bench. D Make alignment mark on container or use set squares with explanation of use. E Use LEDs outside the torch/remove glass from torch. F Use optical bench or draw line/scale/grid on bench or use lens holder to keep lens vertical. 1 mark for each point up to a maximum of 4. 4

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