Cambridge A Level Physics 9702 — 2018 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate an electrical circuit. (a) • You have been provided with the circuit shown in Fig. 1.1. 6 V d.c. A + X + V 1 + Y S 2 Fig. 1.1 • Select one of the groups of parallel resistors and connect it in the component holder. • Connect the resistor R and the component holder in series between X and Y to complete the circuit shown in Fig. 1.2. A + X V 1 Y S R 2 n resistors component in parallel holder Fig. 1.2 • Ensure that switch S is in position 2. • Record the number n of parallel resistors in the component holder. n = ............................................................... • Close switch A. • Record the voltmeter reading V. V = ............................................................... • Open A. [1] (b) • Close A. • Move S to position 1 and start the stopwatch. The voltmeter reading will immediately become negative and then gradually increase. • Stop the stopwatch as soon as the voltmeter reading passes zero and becomes positive. • Record the time t as shown by the stopwatch. t = ............................................................... • Move S to position 2. • Open A. [2] (c) By using different groups of resistors, change n and repeat (b) until you have six sets of values of n and t. 1 Record your results in a table. Include values of in your table. n [9] 1(d) (i) Plot a graph of t on the y‑axis against on the x‑axis. [3] n (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 n are related by the equation a t = + b n 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) 1 1(b) Value of t with unit and in range 1.00–25.00 s. 1 Evidence of repeat readings of t. 1 1(c) Six sets of readings of n and t collected with correct trend (t decreases as n increases) and collected without help from the Supervisor scores 5 marks, five sets scores 4 marks, etc. 5 Range: nmax ⩾ 7 and nmin = 1. 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 / s. There must be no unit for n or 1 n . 1 Consistency: All values of t must be given to 0.01 s or all to 0.1 s. 1 Calculation: Values of 1 n calculated correctly. 1 Question Answer Marks 1(d)(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 in the table must be plotted on the grid. Diameter of points must be ⩽ half a small square (no “blobs”). Points must be accurate to within half a small square in both x and y directions. 1 Quality: General trend of points on graph must be positive. All points in the table (at least 5) must be plotted for this mark to be awarded. It must be possible to draw a straight line that is within ±1.0 s from a straight line in the t direction. 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. Allow one anomalous point only if clearly indicated by the candidate (i.e. circled or labelled). 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 ∆x / ∆y. Both read-offs must be accurate to half a small square in both the x and y directions. Sign of gradient on answer line must match graph. 1 y-intercept: Correct read-off from a point on the line 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 Unit for a is s and unit for b is s. 1

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2 In this experiment, you will investigate the rolling of a sphere along tracks of different widths. (a) (i) Measure and record the diameter d of the sphere. d = ...........................................................[1] (ii) • Measure and record the width w of the narrower track, as shown in Fig. 2.1. narrower track w wooden rails marks board Fig. 2.1 (not to scale) w = ............................................................... • Calculate D 2 where D 2 = d 2 – w 2. D 2 = ............................................................... [1] (b) (i) • Place the board on the bench. Raise the end of the board with the marks by resting it on a wooden block. Place the other wooden block across the lower end of the board, as shown in Fig. 2.2. Secure the blocks in position with small pieces of Blu‑Tack. marks Blu-Tack wooden block bench Blu-Tack wooden block Fig. 2.2 (not to scale) • Measure and record the distance x from the wooden block at the lower end of the board to the mark on the middle rail, as shown in Fig. 2.3. mark x Fig 2.3 (not to scale) x = ...........................................................[1] (ii) • Place the sphere on the narrower track at the position shown in Fig. 2.4. sphere mark Fig. 2.4 (not to scale) • Release the sphere. • Measure and record the time t for the sphere to roll down to the lower wooden block. t = ...........................................................[1] (iii) Estimate the percentage uncertainty in your value of t. percentage uncertainty = ...........................................................[1] (iv) Calculate the final speed v of the sphere, using 2x v = . t v = ...........................................................[1] (v) Justify the number of significant figures you have given for your value of v. ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[1] (c) Repeat (a)(ii), (b)(ii) and (b)(iv) using the wider of the two tracks. w = ............................................................... D 2 = ............................................................... t = ............................................................... v = ............................................................... [3]

Mark scheme: 2(a)(i) Raw value(s) for d with unit and to nearest 0.01 mm. Answer on answer line in range 20.00 mm ⩽ d ⩽ 30.00 mm. 1 2(a)(ii) Value for w with unit and in range 10.0–15.0 mm. 1 2(b)(i) Value for x to nearest mm. Answer in range 55.0 cm ⩽ x ⩽ 65.0 cm. 1 2(b)(ii) Value for t with unit and in range 2.00–4.00 s. 1 2(b)(iii) Percentage uncertainty in t based on an absolute uncertainty in the range 0.2–0.5 s. 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)(iv) Correct calculation of v with consistent unit. 1 2(b)(v) Justification linked to significant figures in x and t. 1 2(c) Second value of w. 1 Second value of t. 1 Quality: t greater for greater w. 1 2(d)(i) Two values of k calculated correctly. 1 2(d)(ii) Valid comment consistent with the calculated values of k, testing against a criterion stated 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 w or large uncertainty in w because w is small or w varies along the length of the track. C Difficult to align sphere in correct starting position. D Sphere won’t start without push/force applied when releasing sphere. E Large percentage uncertainty in t or large uncertainty in t because t is small. 1 mark for each point up to a maximum of 4. 4 2(e)(ii) A Take more readings and plot a graph or calculate more k values and compare (not “repeat readings” on its own). B Use (vernier/digital) calipers (to measure w). C Use a stop/card gate. D Use steeper slope/use steel ball and electromagnet. E1 Use longer track/use shallower slope. E2 Improved method of measuring t, e.g. use light gates at top and bottom/use motion sensor in direction of rolling or video/film/record experiment with timer in view/view frame-by-frame. 1 mark for each point up to a maximum of 4. 4

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