Cambridge A Level Physics 9702 — 2012 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate the variation of current in a circuit for different contact positions on a wire loop. (a) (i) Assemble the circuit of Fig. 1.1. d.c. supply A movable lead X nails nails B A l crocodile loop of clip twisted wire wire Fig. 1.1 (ii) With lead X pressed on to the crocodile clip as shown in Fig. 1.1, adjust the rheostat until the ammeter reading is in the range 160 –190 mA. (iii) Record the ammeter reading I0 when the lead X is pressed on to the crocodile clip. I0 = ...................................................[1] (b) Move lead X and press it on to the wire approximately half way between A and B. Record its distance l from A and record the ammeter reading I. l = ....................................................... I = ....................................................... [1] (c) Repeat (b) with the lead X at different distances from A until you have six sets of values For of l and I. Examiner’s 1 2 Use Include values of and l in your table. I [10] 1 2(d) (i) Plot a graph of on the y-axis against l on the x-axis. [3] I (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ....................................................... y-intercept = ....................................................... [2] For Examiner’s Use (e) The quantities I and l are related by the equation For Examiner’s 1 2 Use = al + b I where a and b are constants. Using your answers from (d)(iii), determine the values of a and b. Give appropriate units. a = ....................................................... b = ....................................................... [2] You may not need to use all of the materials provided. For Examiner’s Use

Mark scheme: 1 (a) (iii) Value for I0 in range 100 to 200 mA, with consistent unit. [1] (b) l in range 40.0 to 60.0 cm, with consistent unit. [1] (c) Six sets of readings of l and I scores 5 marks, five sets scores 4 marks etc. [5] –1 for minor help from Supervisor, –2 for major help. Incorrect trend / no l data / no I data then –1 Range: lmax – lmin ≥ 60 cm. [1] Column headings: [1] Each column heading must contain a quantity and a unit. The unit must conform to accepted scientific comvention e.g. I /mA or I (mA) or 1/ I (mA–1) but not 1/I (mA) and not 1/I (mA)–1. Consistency: [1] All values of l must be given to the nearest mm Significant figures: [1] All values of 1/I must be given to the same number of s.f. (or one more than) the s.f. in the corresponding values of I. Calculated values: [1] Values of 1/I calculated correctly. (d) (i) Axes: [1] Sensible scales must be used, no awkward scales (e.g. 3:10). Scales must be chosen so that the plotted points must 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 3 large squares apart. Plotting of points: [1] All the observations in the table must be plotted on the grid. Diameter of plots must be ≤ half a small square. Points must be plotted accurately. Work to an accuracy of half a small square in both x and y directions. Quality: [1] All points in the table must be plotted (at least 5) for this mark to be scored. Quality is assessed by the scatter of the points about a straight line – all points must be within 0.025 m2 (in the l2 direction) of the line. (ii) Line of best fit: [1] Judge by balance of all the 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. One anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate. Line must not be kinked or thicker than half a square. GCE AS/A LEVEL – October/November 2012 9702 34 (iii) Gradient: [1] Value must be negative if graph gradient is negative. The hypotenuse of the triangle must be greater than half the length of the drawn line. Both read-offs must be accurate to half a small square in both x and y directions. Method of calculation must be correct. y-intercept: [1] Either: Correct read-off from a point on the line, and substitution 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. (e) Value of a = candidate’s gradient and value of b = candidate’s intercept. [1] A value presented as a fraction is not allowed. Unit for a consistent with value, e.g. mA–1cm–2. [1] [Total: 20]

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2 In this experiment, you will investigate the time taken for a ball to roll a fixed distance down an inclined track. (a) You are provided with a straight track with two marks A and B as shown in Fig. 2.1. stand clamp track d tray B A ball bench block Fig. 2.1 Measure and record the distance d between the marks A and B. d = ..................................................[1] (b) Place the ball on the track at A and then adjust the clamp to raise that end of the track as shown in Fig. 2.2, until the ball just starts to roll. ball A B h1 h2 bench Fig. 2.2 (c) (i) Measure and record the height h1 of the track above the bench at A, and the height For Examiner’s h2 of the track above the bench at B. Use h1 = ....................................................... h2 = ....................................................... [1] (ii) The angle that the track makes with the horizontal is θ. Calculate the value of sin θ using the relationship h1 – h2 sin θ = . d sin θ = ...................................................[1] (d) Justify the number of significant figures you have given for your value of sin θ. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[1] (e) Place the ball on the track at A and take measurements to find the time t taken for the ball to roll from rest to B. t = ...................................................[2] (f) Estimate the percentage uncertainty in your value of t. percentage uncertainty = ...................................................[1] (g) (i) Adjust the clamp to raise the track so that h1 increases by approximately 15 mm. For Examiner’s (ii) Repeat (c) and (e). Use h1 = ....................................................... h2 = ....................................................... sin θ = ....................................................... t = ....................................................... [3] (h) It is suggested that the relationship between t and θ is k t = sin θ where k is a constant. (i) Using your data, calculate two values of k. first value of k = ....................................................... second value of k = ....................................................... [1]

Mark scheme: 2 (a) Value of d in range 68.0 to 72.0 cm, with unit [1] (c) (i) h1 and h2 recorded to nearest mm and h1 > h2. [1] (ii) Correct calculation of sinθ. [1] (d) Justification for s.f. linked to s.f in (h1–h2) and s.f. in d. [1] (e) Raw values of t in range 1 to 20 s, with unit. [1] Evidence of repeated measurements for t. [1] (f) Percentage uncertainty in t based on absolute uncertainty of 0.1 or 0.2 or 0.3 s [1] (or half the range if it isn’t zero). Correct method of calculation to get percentage uncertainty. (g) (ii) Second values of h1 and h2. [1] Second value of t. [1] Quality: t smaller for larger (h1–h2). [1] GCE AS/A LEVEL – October/November 2012 9702 34 (h) (i) Correct calculation of two values of k. [1] (ii) Valid conclusion based on the calculated values of k. Candidate must test [1] against a stated criterion. (i) (i) Limitations 4 max. (ii) Improvements 4 max. Do not credit A two results not enough take more readings and plot a ‘repeat readings’ on its own / graph / ‘few readings’ / Calculate more k values and ‘take more readings and compare (calculate) average k’ / ‘only one reading’ B rolling is erratic / marble not too much friction round / track uneven C parallax error in measuring h description of valid method of view at right angles / eye level reducing parallax error in h / use shadow method (e.g. extend mark to wood or track / pointer on rule / travelling microscope*) D difficult to stop stopwatch at use video of marble and clock ‘timegates’/ ‘timergates’ / just correct moment / reaction / lightgate and timer motion ‘reaction time’ time (or human error) linked sensor at end of track / view to stopping of stopwatch frame by frame E small difference between h1 use longer track*/ use vernier caliper and h2 / large uncertainty in (named) more precise method h1– h2 (e.g.travelling microscope*) F difficult to release marble description of mechanical use a clamp / remote without applying a force / method of releasing (e.g. controlled clamp velocity electromagnet with steel / magnetic material ball) G t is small/ large uncertainty in use longer track*/ increase d human reaction error t / ball moves fast so difficult to time accurately * only credited once each. Do not allow ‘repeated readings’ Do not allow ‘use a computer to improve the experiment’ [Total: 20]

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