Cambridge A Level Physics 9702 — 2017 May/June Paper 3 · Variant 4

1 In this experiment, you will investigate the oscillation of a mass-spring system. (a) Assemble the apparatus as shown in Fig. 1.1, with the rods of both clamps at an equal height of approximately 50 cm above the bench. spring string boss θ rod of clamp loop mass stand 50 cm hanger h bench Fig. 1.1 (i) The angle between the two lengths of string is θ, as shown in Fig. 1.1. Adjust the positions of the stands so that θ is approximately 165°. Use the two G-clamps to secure the stands to the bench. The stands should remain in these positions for the rest of the experiment. (ii) Add 200 g to the mass hanger. (iii) Record the total mass M of the mass hanger and added mass. M = ...................................................... (iv) Measure and record the height h of the bottom of the mass hanger above the bench. h = ................................................ cm (v) Pull down the mass hanger through a distance of approximately 2 cm. Release the mass hanger so that it oscillates vertically. Determine the period T of the vertical oscillations. T = ...............................................s [2] (b) Change M and repeat (a)(iii), (a)(iv) and (a)(v) until you have six sets of values of M, h and T. Record your results in a table. Include values of T 3 in your table. [10] (c) (i) Plot a graph of T 3 on the y-axis against h 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 h are related by the equation T 3 = a h + 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)(v) Value of T in the range 0.10–0.90 s. 1 Evidence of repeated readings. Must see nT repeated where n ⩾ 5. 1 1(b) Six sets of readings of M, h and T showing the correct trend and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: Mmax ⩾ 450 g and Mmin ⩽ 200 g. 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. T 3 / s3. 1 Consistency: All values of h must be given to the nearest mm. 1 Significant figures: Significant figures for every value of T 3 must be the same as (or one greater than) the s.f. of raw times as recorded in table. 1 Calculation: Values of T 3 calculated correctly. 1 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 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 plotted to an accuracy of half a small square. 1 Quality: All points in the table must be plotted (at least 5) for this mark to be awarded. It must be possible to draw a straight line that is within ± 1.0 cm (to scale) of all the plotted points in the h direction. 1 Question Answer Marks 1(c)(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. There must be at least five points left after the anomalous point is disregarded. Lines must not be kinked or thicker than half a square. 1 1(c)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct. Do not allow ∆x / ∆y. 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 accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at h = 0, accurate to half a small square in y direction. 1 1(d) Value of a = candidate’s gradient and value of b = candidate’s intercept. The values must not be fractions. 1 Unit for a correct (e.g. s3 cm–1). Unit for b is s3. 1

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2 In this experiment, you will investigate the equilibrium position of a pivoted wooden strip and determine the density of water. (a) Assemble the apparatus as shown in Fig. 2.1. The nail should pass through the hole in the wooden strip and be held in the boss. The bottom of the plastic pipe should be approximately 2 cm above the bottom of the container. Position the string loop with paper clips so that the wooden strip is parallel to the bench. stand string loop x0 boss string loop wooden strip nail paper clips plastic pipe water plumb-line container 2 cm bench Fig. 2.1 (not to scale) The distance from the nail to the string loop holding the paper clips is x0, as shown in Fig. 2.1. Measure and record x0. x0 = ........................................... cm [1] (b) (i) Move the string loop holding the paper clips approximately 4 cm further from the nail. Let the wooden strip settle at an angle, as shown in Fig. 2.2. x φ Fig. 2.2 (not to scale) (ii) Measure and record the new distance x from the nail to the string loop holding the paper clips, as shown in Fig. 2.2. x = ........................................... cm [1] (iii) Measure and record the larger angle φ between the wooden strip and the plumb- line, as shown in Fig. 2.2. φ = .............................................. ° [1] (iv) Calculate (φ – 90°). (φ – 90°) = ................................................... ° (v) Estimate the percentage uncertainty in your value of (φ – 90°). percentage uncertainty = ..................................................[1] (c) (i) Move the string loop holding the paper clips approximately 3 cm further from the nail. Let the wooden strip settle at a new angle. (ii) Repeat (b)(ii), (b)(iii) and (b)(iv). x = ................................................ cm φ = ................................................... ° (φ – 90°) = ................................................... ° [3] Question 2 continues on page 10.

Mark scheme: 2(a) Value for x0 to nearest 0.1 cm. 1 2(b)(ii) x greater than x0. 1 2(b)(iii) Raw θ in range 91–110° and recorded to nearest degree. 1 2(b)(v) Absolute uncertainty in (φ – 90°) of 2–5° and correct method of calculation to obtain percentage uncertainty. If repeated readings of φ have been taken, then the absolute uncertainty can be half the range (but not zero) only if working shown clearly. 1 2(c)(ii) Second value of x. 1 Second value of φ. 1 Quality: second value of φ ⩾ first value of φ. 1 2(d)(i) Two values of k calculated correctly. 1 2(d)(ii) Justification for s.f. in k linked to s.f. in θ, x and x0. 1 2(d)(iii) Valid comment consistent with calculated values of k, testing against a criterion specified by the candidate. 1 2(e)(ii) Raw value(s) of D and d recorded to the nearest 0.1 cm. 1 2(e)(iv) Value of ρ calculated correctly. 1 Question Answer Marks 2(f)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Difficult to get/adjust wooden strip so that it is horizontal/parallel to bench. C Difficulty when measuring x (or x0), with reason e.g. parallax error/thickness of string/difficult to judge centre of nail. D Difficult to measure angle with reason, e.g. parallax error/hard to hold protractor steady/hard not to touch wooden strip/difficult to align protractor correctly. (Do not credit parallax error twice for both C and D.) E Large (percentage) uncertainty in (φ – 90°) or (φ – 90°) is small. F Difficult to measure D (or d) with reason linked to use of ruler. 1 mark for each point up to a maximum of 4. 4 2(f)(ii) A Take more readings and plot a graph/take more readings and compare k values (not “repeat readings” on its own). B Use thinner nail/fulcrum/prism. C Mark a scale on the wooden strip/use a thinner string. D Hold protractor in a clamp/ take photograph and measure angle on photo/ trigonometric method with detail e.g. measure height(s) of end(s) of wooden strip E Method to increase (φ – 90°) e.g. more paper clips/larger values of x/move pipe and pivot closer. F Use vernier/digital calipers/travelling microscope. 1 mark for each point up to a maximum of 4. 4

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