Cambridge A Level Physics 9702 — 2013 Oct/Nov Paper 5 · Variant 2

1 An aluminium ring is placed on a coil with the rod of a metal retort stand passing through For their centres, as shown in Fig. 1.1. Examiner’s Use aluminium ring when alternating current applied to coil h metal retort stand aluminium ring with zero current applied to coil coil Fig. 1.1 When an alternating current of frequency f is applied to the coil, the ring rises until it is in equilibrium at a height h above the coil. It is suggested that the relationship between h and f is h = kf n where k and n are constants. Design a laboratory experiment to test the relationship between h and f and determine values for k and n. 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 For problem data collection analysis considerations detail Examiner’s Use

Mark scheme: 1 Planning (15 marks) Defining the problem (3 marks) P f is the independent variable or vary f. [1] P h is the dependent variable or measure h. [1] P Keep current in coil constant. [1] Methods of data collection (5 marks) M Labelled diagram of apparatus: including working circuit with a.c. supply, coil, stand and ring. [1] M Signal generator (or variable frequency power generator). [1] M Measure h with a rule/calipers. [1] M Measure f using oscilloscope/read off signal generator. [1] M Measure h from opposite sides of the ring (and determine mean)/wait for ring to stabilise. [1] Method of analysis (2 marks) A Plot a graph of lg h against lg f. (Allow ln – ln graphs.) [1] A k = 10y-intercept and n = gradient. [1] Safety considerations (1 mark) S Reasoned method to prevent the coil overheating – switch off when not in use. Or reasoned method to prevent injury from hot coil – do not touch hot coil, use gloves. Do not allow “small currents”. [1] Additional detail (4 marks) D Relevant points might include [4] 1 Use iron/steel retort stand 2 Method to keep current constant 3 Method to determine period from oscilloscope using time-base 4 When using oscilloscope, f = 1/T 5 Use coil of many turns/large current to have measurable heights 6 Logarithmic equation e.g. lg h = n lg f + lg k 7 Relationship is valid if a straight line is produced Do not allow vague computer methods. [Total: 15] GCE AS/A LEVEL – October/November 2013 9702 52

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2 A student is investigating resonance of the air column in a tube using the apparatus shown in For Fig. 2.1. Examiner’s Use tuning fork d tube water Fig. 2.1 For different tuning forks, the water level is adjusted until resonance occurs. For each tuning fork, the frequency f and distance d are recorded. Question 2 continues on the next page. It is suggested that f and d are related by the equation For Examiner’s v Use 4 (d + k ) = f where v is the speed of sound in air and k is a constant. 1(a) A graph is plotted of d on the y-axis against on the x-axis. Determine expressions for f the gradient and y-intercept in terms of k and v. gradient = ..................................................... y-intercept = ..................................................... [1] (b) Values of f and d are given in Fig. 2.2. f / Hz d / cm 320 24.5 ± 0.5 340 23.0 ± 0.5 378 20.5 ± 0.5 428 18.0 ± 0.5 480 16.0 ± 0.5 512 15.0 ± 0.5 Fig. 2.2 1 Calculate and record values of / 10–3 s in Fig. 2.2. [2] f 1(c) (i) Plot a graph of d / cm against / 10–3 s. Include error bars for d. [2] f (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] For 25 Examiner’s d / cm Use 24 23 22 21 20 19 18 17 16 15 14 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 1 / 10–3 s f

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Mark Expected Answer Additional Guidance (a) A1 Gradient = v/4 y-intercept must be negative. y-intercept = –k (b) T1 1/f / 10–3 s Column heading. Allow equivalent unit. e.g. f –1/ 10–3 Hz–1 or 1/f (10–3 s) T2 A mixture of 3 s.f. and 4 s.f. is allowed. 3.13 or 3.125 2.94 or 2.941 2.65 or 2.646 2.34 or 2.336 2.08 or 2.083 1.95 or 1.953 (c) (i) G1 Six points plotted correctly Must be less than half a small square. Ecf allowed from table. Penalise “blobs”. U1 All error bars in d plotted Must be within half a small square. Each error correctly bars should be five small squares (ii) G2 Line of best fit If points are plotted correctly then lower end of line should pass between (2.06, 16) and (2.10, 16) and upper end of line should pass between (3.12, 24.5) and (3.16, 24.5). G3 Worst acceptable straight Line should be clearly labelled or dashed. Should line. pass from top of top error bar to bottom of bottom Steepest or shallowest error bar or bottom of top error bar to top of possible line that passes bottom error bar. Mark scored only if error bars through all the error bars. are plotted. (iii) C1 Gradient of best fit line 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. U2 Uncertainty in gradient Method of determining absolute uncertainty Difference in worst gradient and gradient. (iv) C2 y-intercept – must be Check substitution in y = mx + c. negative Allow ecf from (c)(iii). FOX does not score. Should be about –1 (–0.35 to –1.33). U3 Uncertainty in y-intercept Check substitution in y = mx + c. Difference in worst y-intercept and y-intercept. Allow ecf from (c)(iv) but FOX does not score. GCE AS/A LEVEL – October/November 2013 9702 52 (d) C3 k = – y-intercept cm or m Method required with appropriate unit. v = 4 × gradient cm s–1 or Do not penalise POT. Allow ecf from (c)(iii) and m s–1 (iv). U4 Determines absolute Uncertainty k = uncertainty in y-intercept. uncertainties in k and v Uncertainty in v = 4 × uncertainty in gradient. (e) (i) C4 Between 250 and 260 given Must be in range. Check method. to 2 or 3 s.f. (ii) U5 Percentage uncertainty in f Absolute uncertainties in d and k must be added. ∆(d + k) = ∆d + ∆k % uncertainty in v + % uncertainty in (d + k). [Total: 15] Uncertainties in Question 2 (c) (iii) Gradient [U2] Uncertainty = gradient of line of best fit – gradient of worst acceptable line Uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (c) (iv) y-intercept [U3] 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) [U4] Uncertainty in k = uncertainty in y-intercept Uncertainty in v = 4 × uncertainty in gradient (e) [U5] max v max gradient max f = = 4(min d + min k ) (min d + min k ) min v min gradient min f = = 4(max d + max k ) 4(max d + max k ) Percentage uncertainty = % uncertainty in v + % uncertainty in (d + k) Percentage uncertainty = % uncertainty in gradient + % uncertainty in (d + k)

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