Cambridge A Level Physics 9702 — 2019 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will investigate the motion of a pendulum consisting of a chain of paper clips and a sphere of modelling clay. (a) Set up the apparatus as shown in Fig. 1.1. • clamp nail n paper clips overhanging boss cork stand tape sphere of modelling clay bench Fig. 1.1 Suspend the chain of paper clips from the nail by one of the clips with n clips overhanging. • Count and record n. • n = ............................................................... Pull the sphere to the side through a short distance, as shown in Fig. 1.2.• Fig. 1.2 Release the sphere. The sphere will oscillate.• Determine the period T of these oscillations.• T = ......................................................... [1] (b) Vary n by placing the nail through different clips in the chain. Measure and record n and T. Repeat until you have six sets of values. Record your results in a table. Include values of T 2 in your table. [10] (c) (i) Plot a graph of T 2 on the y-axis against n 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 n are related by the equation T 2 = Pn + Q where P and Q are constants. Using your answers in (c)(iii), determine the values of P and Q. Give appropriate units. P = ............................................................... Q = ............................................................... [2] (e) Theory suggests that P is proportional to the length of a paper clip and that Q is proportional to the total length of the chain. The experiment is repeated using a chain consisting of 30 paper clips of the same length as those used in your experiment. For this experiment, draw a second line on the graph to show the expected results. Label this line W. [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of T on the answer line in the range 1.0–2.0 s with unit. 1 1(b) Six sets of readings of n and T (different values) with the correct trend and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc. 5 Range: n values include n = 2 or less and n = 13 or more. 1 Column headings: Each column heading must contain a quantity, a unit where appropriate and a separating mark. The presentation of quantity and unit must conform to accepted scientific convention e.g. T / s, T2 / s2 and n has no unit. 1 Consistency: Raw values of time must all 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 time values. 1 Calculation: Correct calculation of T2. 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 must 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 graph must be negative. It must be possible to draw a straight line that is within ±1 (to scale) on the n-axis of all plotted points. 1 Question Answer Marks 1(c)(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. One anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate. There must be at least 5 points left after the anomalous point is disregarded. Lines 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. The method of calculation must be correct e.g. not ∆x / ∆y. The sign of the gradient on the answer line must match the graph. 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 n = 0 accurate to half a small square. 1 1(d) Value of P = candidate’s gradient and value of Q = candidate’s intercept. The values must not be fractions. 1 Unit for P is s2 and unit for Q is s2. 1 1(e) Line W is drawn with the same gradient and a larger y-intercept. 1

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2 In this experiment, you will investigate how the force of attraction between two bar magnets depends on their separation. (a) (i) Place magnet A on the wooden board as shown in Fig. 2.1. • wooden board magnet A A bench Fig. 2.1 Raise the end of the board until the magnet just starts to move down the board, as • shown in Fig. 2.2. A α bench Fig. 2.2 The angle between the bench and the board when the magnet just starts to move • is α. Measure and record α. α = ........................................................° [2] (ii) Estimate the percentage uncertainty in your value of α. percentage uncertainty = ......................................................... [1] (b) You have been provided with a small block of wood as shown in Fig. 2.3. x Fig. 2.3 The smallest dimension of the block is x. Measure and record x. x = ......................................................... [1] (c) Use some of the adhesive putty to secure the block to the board on the line as shown in • Fig. 2.4. Use some of the adhesive putty to secure magnet B to the board at a distance y from the • block, where y is approximately 5 mm. Place magnet A on the board as shown in Fig. 2.4 so that the magnets are attracting • each other. x magnet A block magnet B A B line y Fig. 2.4 Raise the end of the board until magnet A starts to move down the board. • The angle at which A just starts to move is β, as shown in Fig. 2.5. If A does not move • down the board for any angle of the board, gradually increase y until it does move. B A β bench Fig. 2.5 Measure and record β. • β = ........................................................° [1] (d) (i) Measure and record y. • y = ............................................................... Calculate (x + y)2. • (x + y)2 = ............................................................... [1] (ii) Justify the number of significant figures that you have given for your value of (x + y)2. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1]

Mark scheme: 2(a)(i) 1 Evidence of repeated α. 1 2(a)(ii) Percentage uncertainty based on an absolute uncertainty in α in the range 2–5°. 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(b) Value(s) of raw x to the nearest mm with unit. 1 2(c) Value of β > α. 1 2(d)(i) Correct calculation of (x + y)2. 1 2(d)(ii) Justification for s.f. in (x + y)2 linked to s.f. in (x + y). 1 2(e) Second value of x. 1 Second value of β. 1 Quality: second value of β greater than α and second value of β < first value of β. 1 2(f)(i) Two values of k calculated correctly. 1 2(f)(ii) Valid comment consistent with the calculated values of k, testing against a criterion stated by the candidate. 1 Question Answer Marks 2(g)(i) A Too few readings/(only) two readings not enough to draw a (valid) conclusion (not ‘not enough for accurate results’, ‘few readings’). B Difficulty in measuring angle(s) or α or β with a reason e.g. difficult to hold board or protractor steady/board or protractor held by hand/difficult to hold board and protractor at same time. C Difficulty with raising the board e.g. difficult to raise board evenly/jerks/suddenly rises and consequently board shakes causing magnet to move/difficult to change the angle by small increments (idea of sensitivity). D Base of board slides/slips along bench. E Magnet crashes into bench (and could affect strength of magnet). F Difficulty with board surface e.g. surface may not be uniformly smooth/may be uneven. 1 mark for each point up to a maximum of 4. 4 2(g)(ii) A Take more readings and plot a graph or take more readings and compare k values (not ‘repeat readings’ on its own). B Improved method of supporting protractor or board e.g. clamp protractor/clamp board or Detailed method of using trigonometry e.g. measure elevation (o) and length of board (a) calculate sin angle = o / a or Film/video/record with protractor in view. C Method described to increase the angle in smaller increments e.g. lab jack support/string attached to board and a pulley with handle. D Method of fixing base of board e.g. adhesive putty/heavy block. E Improved method to protect magnets e.g. place foam around bench/wooden barrier. F Method to provide a smooth surface e.g. named smooth material e.g. glass or valid method e.g. sand board. 1 mark for each point up to a maximum of 4. 4

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