Cambridge A Level Physics 9702 — 2017 Oct/Nov Paper 3 · Variant 1

1 In this experiment, you will investigate the motion of a Y-shaped pendulum. (a) You have been provided with two pieces of string. The longer piece of string has a loop at each end. The shorter piece of string is attached to a bob. Set up the apparatus as shown in Fig. 1.1. Attach the shorter string to the middle of the longer string with a knot. Ensure the two rods of the clamps are at the same height above the bench. Position the stands approximately 35 cm apart. boss boss rod of clamp rod of clamp θ longer string knot shorter string stand stand bob ≈ 35 cm bench Fig. 1.1 The angle θ is the angle between the two halves of the longer string. (b) Measure and record θ. θ = ..................................................[1] (c) Pull the bob a short distance towards you. Release the bob. The bob will oscillate. Determine the period T of these oscillations. T = ..................................................[1] (d) Vary the distance between the stands and repeat (b) and (c) until you have six sets of values of θ and T. θi 2 Record your results in a table. Include values of cos and T in your table. c 2 m [10] 2 θi(e) (i) Plot a graph of T on the y-axis against cos on the x-axis. [3] c 2 m (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ...................................................... y-intercept = ...................................................... [2] (f) It is suggested that the quantities T and θ are related by the equation 2 θi T = P cos + Q c 2 m where P and Q are constants. Using your answers in (e)(iii), determine the values of P and Q. Give appropriate units. P = ...................................................... Q = ...................................................... [2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(b) 1 1(c) Value of T in range 0.80–2.00 s with unit. 1 1(d) Six sets of readings of θ (different values) and time showing the correct trend (T increases as θ decreases) and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: θ ⩾ 120° and θ ⩽ 60°. 1 Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of the quantity and the unit must conform to accepted scientific convention e.g. T2 / s2 and θ / °. No unit for cos (θ / 2). 1 Consistency: All raw values of time must be given to the nearest 0.1 s or all to the nearest 0.01 s. 1 Significant figures: All values of T2 must be given to the same number of s.f. as (or one more than) the number of s.f. in raw values of time. If raw times recorded to nearest 0.01 s, allow number of s.f. of T2 to be one less than the number of s.f. of the raw times. 1 Values of cos (θ / 2) calculated correctly. 1 Question Answer Marks 1(e)(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 (at least 5) must be plotted on the grid for this mark to be awarded. It must be possible to draw a straight line that is within 0.05 on the cos (θ / 2) axis (x-axis) of all plotted points. 1 1(e)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate’s line (at least 5). 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 small square. 1 1(e)(iii) Gradient: The hypotenuse of the triangle used should 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. The method of calculation must be correct. 1 y-intercept: Check 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 in the y direction. 1 Question Answer Marks 1(f) Value of P = candidate’s gradient and value of Q = candidate’s intercept. The values must not be fractions. 1 Units for P and Q correct (s2). 1

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2 In this experiment, you will investigate the appearance of a line viewed through a jar containing water. (a) You have been provided with an empty glass jar. The thickness of the glass is t. Measure and record t. t = ............................................ cm [1] (b) (i) The outer diameter of the glass jar is d as shown in Fig. 2.1. d Fig. 2.1 Measure and record d. d = ..................................................[1] (ii) Calculate the inner diameter D of the jar where D = d – 2t. D = ...................................................... (c) (i) Add water to the jar until it is approximately three-quarters full. (ii) The height h of water in the jar is shown in Fig. 2.2. water h bench Fig. 2.2 Measure and record h. h = ..................................................[1] (iii) Calculate the approximate volume V of water in the jar using πD2h V = . 4 V = ..................................................[1] (iv) Justify the number of significant figures that you have given for your value of V. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1] (d) Draw a straight line of approximate length 25 cm in the centre of the A4 sheet of paper. (e) (i) Place the jar centrally on the line as shown in Fig. 2.3. line top of jar Fig. 2.3 Look down on the jar from directly above. The line should appear to pass through the centre of the jar as an unbroken straight line. (ii) Move your head backwards and forwards. When viewed through the water, the line (shown dotted) appears to move as shown in Fig. 2.4. Fig. 2.4 (iii) Place the nails on the line either side of the jar as shown in Fig. 2.5. line nail nail top of jar Fig. 2.5 (iv) For a particular height of the nails, the nails and the line viewed through the water appear to move together when you move your head backwards and forwards. Raise the nails to this height.

Mark scheme: 2(a) Value of t in the range 2–9 mm, t to the nearest 0.01 cm or 0.001 cm. 1 2(b)(i) Value of d to the nearest 0.1 cm or better. 1 2(c)(ii) Value of h with unit. 1 2(c)(iii) Correct calculation of V with consistent unit. 1 2(c)(iv) Justification for s.f. in V linked to s.f. in (d – 2t) and h. Allow d, t and h or allow d and h. 1 2(e)(v) Value of y with evidence of repeats. 1 2(f) Percentage uncertainty in y based on absolute uncertainty of 2–8 mm. 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(g) Second value of h. 1 Second value of y. 1 Quality: second value of y less than first value of y. 1 Question Answer Marks 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 2(i)(i) A Two readings/too few readings/only two readings not enough to draw a (valid) conclusion. B Difficult to measure t with reason e.g. screw thread in way, curved surface, thickness not the same throughout the glass. C Inaccurate V with reason e.g. non-cylindrical shape of jar/equation gives an approximate value. D Difficult to judge correct position of nails. E Difficult to measure y with reason e.g. holding the nail and ruler in position. 1 mark for each point up to a maximum of 4. 4 2(i)(ii) A Take more readings (for different volumes) and plot a graph/take more values of k and compare. B Improved method of measuring t directly e.g. travelling microscope. C Improved method of measuring volume e.g. fill with water and use a measuring cylinder/measure circumference with string to calculate diameter to put into equation for volume. D Use optical pins/thinner nails. E Have scale on side of jar/place both nails on lab jacks/use marker pen instead of nails/clamp ruler/use a marker to mark position of nail. 1 mark for each point up to a maximum of 4. 4

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