Cambridge A Level Physics 9702 — 2021 Oct/Nov Paper 3 · Variant 6

1 In this experiment, you will investigate the oscillations of a wooden strip. (a) (i) ● Assemble the apparatus as shown in Fig. 1.1 with the nail held securely in the boss. boss L nail wooden strip M string loop string mass spring string stand weight bench Fig. 1.1 ● Hang the mass labelled M midway between the nail and the end of the strip. ● Adjust the height of the boss so that the strip is parallel to the bench. ● Move the weight so that the spring is vertical. ● L is the distance between the nail and the string loop attached to M, as shown in Fig. 1.1. Measure and record L. L = ......................................................... [1] (ii) ● Pull the free end of the strip down by approximately 2 cm. Release the strip so that it oscillates. ● Take measurements to determine the period T of the oscillations. T = ....................................................... s [2] (b) ● Move M along the strip and adjust the apparatus so that the strip is parallel to the bench. ● Measure L and determine T. ● Repeat until you have six sets of values of L and T. Record your results in a table. Include values of L2 and T2 in your table. [9] (c) (i) Plot a graph of T2 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] (d) It is suggested that the quantities T and L are related by the equation T2 = aL2 + b where a and b are constants. Use your answers in (c)(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)(i) Value of L with unit and in the range 20.0–25.0 cm. 1 1(a)(ii) Value of T in range 0.80–1.20 s. 1 Repeats: at least two measurements of at least 5T. 1 1(b) Six sets of readings of L and T with correct trend and without help from the Supervisor scores 4 marks, five sets scores 3 marks, etc. 4 Range: Lmin ⩽ 12.0 cm and Lmax ⩾ 40.0 cm. 1 Column headings: 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. L2 / cm2. 1 Consistency: All values of raw L must be given to the nearest mm. 1 Significant figures: Values of L2 should be to the same number of s.f. as (or one more than) the number of s.f. in the corresponding value of L. 1 Calculation: Values of L2 calculated correctly. 1 Question Answer Marks 1(c)(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 the x and y directions. Axes 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 in both x and y directions. 1 Quality: All points in the table (at least 5) must be plotted on the grid. Trend of points on graph must be correct. It must be possible to draw a straight line that is within ± 0.02 m2 on the L2 axis (x-axis) of all plotted points. 1 1(c)(ii) Line of best fit: Judge by the 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. Allow one anomalous point only if clearly indicated (i.e. circled or labelled) by the candidate. There must be at least five points left after the anomalous point is disregarded. Line must not be kinked or thicker than half a small square. 1 1(c)(iii) Gradient: 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, e.g. Δy / Δx. Gradient sign on answer line matches graph drawn. 1 y-intercept: 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 L2 = 0, accurate to half a small square. 1 Question Answer Marks 1(d) a equal to candidate’s gradient and b equal to candidate’s intercept. Values must not be written as fractions. 1 Units for a (e.g. s2 cm–2) and b (e.g. s2) are correct. 1

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2 In this experiment, you will investigate the amount of air needed to lift an underwater load. (a) You are provided with a syringe attached to a long tube containing a wire. ● Bend the end of the tube as shown in Fig. 2.1. tube 8 cm to syringe wire Fig. 2.1 ● Pull the plunger of the syringe to the 50 cm3 mark (1 cm3 = 1 ml). ● Bend the tube and hook it over the container so that the end is approximately 11 cm above the bottom of the container, as shown in Fig. 2.2. syringe container tube containing wire water plunger air . 11 cm tray Fig. 2.2 (i) You have been provided with a set of metal rings. Take measurements to determine the average thickness t of the rings. Show your working. t = ................................................... cm [1] (ii) Measure and record the inner diameter d1 and the outer diameter d2 of one of the metal rings, as shown in Fig. 2.3. d1 d2 Fig. 2.3 d1 = ......................................................... cm d2 = ......................................................... cm [1] (iii) Calculate the volume VR of a metal ring using πt(d22 – d12) VR = 4 . VR = .................................................. cm3 [1] (iv) Justify the number of significant figures that you have given for your value of VR. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (b) You have been provided with a paper clip and a plastic cup with string attached. (i) ● Bend the paper clip into a hook shape as shown in Fig. 2.4. Add 8 metal rings to the paper clip and hook it onto the string loop, as shown in Fig. 2.4. top string cup string loop paper clip rings Fig. 2.4 ● Lower the cup into the water. Ensure that the cup is completely filled with water. ● Use the top string to position the cup over the end of the tube, as shown in Fig. 2.5. top string Fig. 2.5 ● Record the initial reading x1 from the syringe scale. x1 = .................................................. cm3 [1]

Mark scheme: 2(a)(i) Evidence of measuring a multiple of t and then dividing. 1 2(a)(ii) Values of d1 and d2 to nearest 0.1 cm. 1 2(a)(iii) Correct calculation of VR. 1 2(a)(iv) Justification based on significant figures in t, d1 and d2. 1 2(b)(i) Value of x1 to nearest 1 cm3 and in range 45–55 cm3. 1 2(b)(ii) Value of x2 less than x1. 1 Correct calculation of VA. 1 2(b)(iii) Percentage uncertainty based on an absolute uncertainty in the range 2–4 cm3. 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. 1 2(c) Second values for x1 and x2. 1 Second VA > first VA. 1 2(d)(i) Two values of k calculated correctly. The final values must not be written as fractions. 1 2(d)(ii) Valid comment consistent with the calculated values of k, testing against a criterion specified by the candidate. 1 Question Answer Marks 2(e)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Large percentage uncertainty in t/d1/d2/VR. C Difficult to remove all air from cup at start/air leaks out of cup when operating syringe. D Difficult to judge when cup starts to rise or difficult to operate plunger smoothly or difficult to stop plunger when cup starts to rise. E Cup sticks to wall of container. F Volume (or mass) of cup/paper clip/string not taken into account. G x (or VA) values affected by water getting into tube. 1 mark for each point up to a maximum of 4. 4 Question Answer Marks 2(e)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). B Use vernier calipers/digital calipers/micrometer/travelling microscope. C Description of workable method of removing air. D Video/film/record with syringe in view or mark cup starting position on container. E Use wider container. F Method of finding volume of cup/string/paper clip or method of measuring mass of cup/string/paper clip e.g. top pan balance. G Method of removing water from tube or use new tube. 1 mark for each point up to a maximum of 4. 4

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