Cambridge A Level Physics 9702 — 2014 May/June Paper 5 · Variant 1

1 A ball rolls forwards and backwards on a curved track as shown in Fig. 1.1. flexible track ball Fig. 1.1 It is suggested that the period T of the oscillations is related to the radius r of the ball and the radius of curvature C of the track by the relationship 2 28p2 T = (C – r ) 5g where g is the acceleration of free fall. You are provided with a flexible track. Design a laboratory experiment to test the relationship between T and r. Explain how your results could be used to determine a value for C. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to (a) the procedure to be followed, (b) the measurements to be taken, (c) the control of variables, (d) the analysis of the data, (e) the safety precautions to be taken. 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Defining the Methods of Method of Safety Additional problem data collection analysis considerations detail

Mark scheme: 1 Planning (15 marks) Defining the problem (3 marks) P r is the independent variable or vary r. [1] P T (or t) is the dependent variable or measure T (or t). [1] P Keep the radius of curvature (of the track) or C constant (or radius of track constant). Do not allow “use same track”. [1] Methods of data collection (5 marks) M Diagram showing ball in a (curved) track with supports for track, e.g. retort stands. Minimum of two labels (from ball, track, supports; not stopwatch, bench, micrometer). Supports making contact with track higher than ball / at least half way up. [1] M Measure time using stopwatch or light gates and timer or datalogger with motion sensor. Detail needed for video camera. [1] M Use many oscillations (at least 10 or at least 10 s of timing) and determine T = t / n. [1] M Measure diameter (radius) of ball with a micrometer / vernier calipers. Do not allow travelling microscope. [1] M radius = diameter / 2. [1] Method of analysis (2 marks) A Plot a graph of T 2 against r (or r against T 2) Do not allow log graphs. [1] 5 g y − intercept A C = y-intercept × = (or for r against T 2, C = y-intercept) [1] 2 gradient 28 π Safety considerations (1 mark) S Precaution linked to ball escaping on to floor, e.g. use barrier / safety screen / sand tray to prevent balls rolling on to floor. [1] GCE AS/A LEVEL – May/June 2014 9702 51 Additional detail (4 marks) D Relevant points might include [4] 1 Add weights to / G-clamp retort stands 2 Keep the material / density of the ball constant 3 Use of fiducial marker near centre of track / mark on the track 4 Clean track / balls. Do not allow oil the track. 5 Repeat measurements of t (for each ball) and average 6 Repeat measurement for d (or r) and average 7 Relationship is valid if straight line, provided plotted graph is correct 8 Relationship is valid if straight line not passing through origin or has an intercept, provided plotted graph is correct (any quoted expression must be correct, e.g. 28 π 2C y-intercept = ) 5 g Do not allow vague computer methods. [Total: 15] GCE AS/A LEVEL – May/June 2014 9702 51

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2 A student is investigating a circuit containing an operational amplifier (op-amp). The circuit is set up as shown in Fig. 2.1. R +15 V P – Q E + –15 V V Fig. 2.1 The op-amp is connected to a +15 V and –15 V power supply. An experiment is carried out to investigate how the reading V on the voltmeter varies with the resistance Q of resistor Q. It is suggested that V and Q are related by the equation J 1 1 N V = –ER KK + OO P Q L P where E is the e.m.f. of the cell, P is the resistance of resistor P and R is the resistance of resistor R. V 1 (a) A graph is plotted of on the y-axis against on the x-axis. E Q Determine expressions for the gradient and the y-intercept in terms of P and R. gradient = ...................................................... y-intercept = ...................................................... [1] (b) The e.m.f. E of the cell has a value of 1.6 ± 0.1 V. Values of V and Q are given in Fig. 2.2. Q / 103 Ω V / V 1 / 10–3 Ω–1 V Q E 0.15 –8.2 ± 0.1 0.22 –6.0 ± 0.1 0.33 –4.4 ± 0.1 0.50 –3.3 ± 0.1 0.66 –2.8 ± 0.1 0.90 –2.4 ± 0.1 Fig. 2.2 1 V Calculate and record values of / 10–3 Ω–1 and in Fig. 2.2. Q E V Include the absolute uncertainties in . [3] E V 1 V(c) (i) Plot a graph of against / 10–3 Ω–1. Include error bars for . [2] E Q E (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the line of best fit. Include the uncertainty in your answer. gradient = ..................................................[2] 1 / 10–3 Ω–1 Q 0 1 2 3 4 5 6 7 –1.0 –1.5 V E –2.0 –2.5 –3.0 –3.5 –4.0 –4.5 –5.0 –5.5 –6.0

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Mark Expected Answer Additional Guidance (a) A1 gradient = –R Must be negative. y-intercept = –R/P (b) T1 Allow a mixture of significant figures. T2 6.7 or 6.67 –5.1 or –5.13 T1 and T2 must be table values. Ignore “–” omissions. 4.5 or 4.55 –3.8 or –3.75 3.0 or 3.03 –2.8 or –2.75 2.0 or 2.00 –2.1 or –2.06 1.5 or 1.52 –1.8 or –1.75 1.1 or 1.11 –1.5 or –1.50 U1 From ± 0.3 or ± 0.4 to ± 0.1 or ± 0.2 Allow more than one significant figure. (c) (i) G1 Six points plotted correctly Must be within half a small square. Penalise “blobs”. Ecf allowed from table. U2 Error bars in V / E plotted correctly All error bars to be plotted. Must be accurate to less than half a small square. (ii) G2 Line of best fit If points are plotted correctly then lower end of line should pass between (6.4,–5.0) and (6.6,–5.0) and upper end of line should pass between (1.0,–1.5) and (1.2,–1.5). G3 Worst acceptable straight line. Line should be clearly labelled or Steepest or shallowest possible line dashed. Should pass from top of top that passes through all the error bars. error bar to bottom of bottom error bar or bottom of top error bar to top of bottom error bar. Mark scored only if all error bars are plotted. (iii) C1 Gradient of best fit line Must be negative. The triangle used should be at least half the length of the drawn line. Check the read offs. Work to half a small square. Do not penalise POT. (Should be about –650.) U3 Uncertainty in gradient Method of determining absolute uncertainty. Difference in worst gradient and gradient. GCE AS/A LEVEL – May/June 2014 9702 51 (iv) C2 Negative y-intercept Must be negative. Check substitution into y = mx + c Allow ecf from (c)(iii). (Should be about –0.8.) FOX does not score. U4 Uncertainty in y-intercept Uses worst gradient and point on WAL. Check method. FOX does not score. (d) (i) C3 P = R / y-intercept Include unit [Ω] for P and R. = –gradient / y-intercept Do not penalise POT. C4 R = gradient in the range 620 to 680 and given to 2 or 3 s.f. (ii) U5 Percentage uncertainty in P Percentage uncertainty in gradient + percentage uncertainty in y-intercept [Total: 15] Uncertainties in Question 2 (c) (iii) Gradient [U3] Uncertainty = gradient of line of best fit – gradient of worst acceptable line Uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (c) (iv) [U4] Uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line Uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept) (d) (i) [U5] Percentage uncertainty in gradient + percentage uncertainty in y-intercept max R max gradient max P = = min y − intercept min y − intercept min R min gradient min f = = max y − intercept max y − intercept

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