Cambridge A Level Physics 9702 — 2020 May/June Paper 3 · Variant 2

1 In this experiment, you will investigate a pendulum made from a wooden strip with masses fixed at one end. (a) Some of the apparatus has been assembled for you. ● Pass the nail through the hole in the strip furthest from the masses. ● Fix the nail securely in the clamp. ● Complete the set-up of the apparatus as shown in Fig. 1.1. clamp stand nail d hooks boss spring ≈ 6 cm ≈ 6 cm holes stand masses wooden strip bench Fig. 1.1 (not to scale) ● The hooks at the ends of the springs should pass through one of the holes in the strip. Position the stands so that the coiled section of each spring is of approximate length 6 cm and the strip is vertical. ● The distance along the strip between the nail and the hole with the hooks is d. Measure and record d. d = ................................................... cm [1] (b) ● Move the bottom of the strip towards one of the stands and release it so that it oscillates. ● Take measurements to determine the period T of these oscillations. T = ...................................................... s [2] (c) Move the hooks to a different hole in the strip. Measure d and T. Repeat until you have six sets of values of d and T. 1 Record your results in a table. Include values of d 2 and 2 in your table. T [9] 1 (d) (i) Plot a graph of 2 on the y-axis against d 2 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] (e) It is suggested that the quantities T and d are related by the equation 1 2 = ad 2 + b T where a and b are constants. Use your answers in (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(a) Value of d in range 5–40 cm. 1 1(b) Value of T in range 0.10–1.50 s. 1 Evidence of repeat readings: at least two values of at least 5T. 1 1(c) Six sets of readings of d and T showing the correct trend and without help from the Supervisor scores 4 marks, five sets scores 3 marks etc. 4 Range: xmin ⩽ 10.0 cm and xmax ⩾ 30.0 cm. 1 Column headings: Each column heading must contain a quantity, a unit and a separating mark where appropriate. The presentation of the quantity and unit must conform to accepted scientific convention e.g. 1 / T 2 (s–2). 1 Consistency: All raw values of d must be given to the nearest mm. 1 Significant figures: Number of significant figures for every value of d2 the same as, or one more than, the number of s.f. in the corresponding value of d. 1 Calculation: Values of d2 calculated correctly. 1 Question Answer Marks 1(d)(i) Axes: Sensible scales must be used, no awkward scales (e.g. 3:10). 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 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. 1 Quality: All points in the table (at least 5) must be plotted on the grid. Trend of points on the graph must be correct. It must be possible to draw a straight line that is within ± 0.20 s–2 on the 1 / T2 axis of all plotted points. 1 1(d)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate’s line (at least 5 points). There must be an even distribution of points either side of the line along the full length. If there are 6 or more points, allow one anomalous point only if clearly indicated by the candidate. Line 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. Do not allow Δx / Δy. 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 and substituted into y = mx + c. 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 at x = 0 accurate to half a small square. 1 Question Answer Marks 1(e) Value of a equal to candidate’s gradient and value of b equal to candidate’s intercept. The values must not be fractions. 1 Units for a (e.g. s–2 cm–2) and b (s–2) correct. 1

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2 In this experiment, you will investigate the bending of a rod under a compressive force. (a) You are provided with two thin rods. Measure and record the length L and diameter d of the longer rod. L = ............................................................... d = ............................................................... [2] (b) ● Assemble the apparatus as shown in Fig. 2.1 using the longer rod. Position the ends of the rod in the shallow holes in the wooden strip and the block. nail held in boss y x string loop stand rod holes newton meter wooden strip block bench Fig. 2.1 ● Adjust the apparatus so that the rod is vertical and the wooden strip is parallel to the bench. ● The distance between the nail and the top of the rod is x and the distance between the nail and the string loop is y, as shown in Fig. 2.1. Measure and record x and y. x = ............................................................... y = ............................................................... [1] (c) ● Slowly pull the newton meter down until the rod bends in the middle by approximately 1 cm, as shown in Fig. 2.2. ≈ 1 cm Fig. 2.2 ● Record the force Fm needed to bend the rod by approximately 1 cm. Fm = ......................................................... [2] (d) Estimate the percentage uncertainty in your value of Fm. Show your working. percentage uncertainty = ......................................................... [1] (e) Calculate the force F exerted on the rod using yFm F = . x F = ......................................................... [1] (f) Justify the number of significant figures you have given for your value of F. ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [1] (g) ● Measure and record the length L and diameter d of the shorter rod. L = ............................................................... d = ............................................................... ● Set up the apparatus as shown in Fig. 2.1 using the shorter rod. ● Adjust the apparatus so that the rod is vertical and the wooden strip is parallel to the bench. ● Repeat (c) and (e). Fm = ............................................................... F = ............................................................... [2]

Mark scheme: 2(a) Value of L to nearest mm, with unit. 1 Value of d to the nearest 0.01 mm and in the range 2.00–5.00 mm, with unit. 1 2(b) Values of x and y, with x < y. 1 2(c) Value for Fm, with unit, to nearest 0.1 N. 1 Evidence of repeated readings of Fm. 1 2(d) Percentage uncertainty in Fm based on an absolute uncertainty of 0.2–0.5 N. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(e) Correct calculation of F. 1 2(f) Justification based on s.f. in Fm, x and y. 1 2(g) Second values of L, d and Fm. 1 Quality: Second Fm > first Fm. 1 2(h)(i) Two values of E calculated correctly. 1 2(h)(ii) Valid comment relating to the calculated values of E, testing against a criterion specified by the candidate. 1 Question Answer Marks 2(i)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to measure 1 cm bend. C Rod bends suddenly (so difficult to stop at 1 cm bend). D (Whole) weight of newton meter not included in Fm. E Large percentage uncertainty in Fm (for longer rod). F Repeat values of Fm differ because rod stays bent. G Difficult to measure deflection and Fm at the same time. 1 mark for each point up to a maximum of 4. 4 2(i)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Clamp ruler/use grid behind rod/workable method using stop. C Use motor/other workable method to pull newton meter slowly. D Zero then weigh newton meter and add to reading, or similar. E Increase x/decrease y (for longer rod). F Provide more identical rods. G Video rod and newton meter and replay. 1 mark for each point up to a maximum of 4. 4

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