Cambridge A Level Physics 9702 — 2015 May/June Paper 5 · Variant 1

1 A student is investigating simple harmonic motion using an electric vibrator. A plate is attached to the top of the electric vibrator. A small mass is placed on the metal plate as shown in Fig. 1.1. metal plate small mass vibrator Fig. 1.1 An alternating potential difference (p.d.) is applied to the vibrator. For a given peak p.d. V, there is a maximum frequency f at which the small mass remains in contact with the plate. The contact between the small mass and plate is lost when the frequency is greater than f. It is suggested that the relationship between f and V is k = π2f 2V where k is a constant. Design a laboratory experiment to test the relationship between f and V. Explain how your results could be used to determine a value for k. 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 V is the independent variable, or vary V and f is the dependent variable, or measure f. Or f is the independent variable, or vary f and V is the dependent variable, or measure V. [1] P Change f (allow V) until the mass leaves/gap between plate. [1] P Keep the position of the mass constant. (Do not allow keep mass constant.) [1] Methods of data collection (5 marks) M Labelled diagram showing signal generator/a.c. supply connected to vibrator with two wires with mass on plate. At least two labels needed. [1] M Voltmeter/c.r.o. connected in parallel with vibrator in a workable circuit. [1] M Measure f or T from signal generator/c.r.o. (Allow detailed use of motion sensor/stroboscope.) [1] M Detail regarding mass leaving the plate: listen to noise, look for gap. [1] M Repeat each experiment for the same value of V (allow f if consistent with above) and average. [1] Method of analysis (2 marks) Plot a graph of: f 2 1 / V f 1 / V lg V lg f A against against against against against against 1 / V f 2 1 / V f lg f lg V or or or or V 1 / f 2 V 1 / f against against against against [1] 1 / f 2 V 1 / f V k = π 2 k = π 2 k = k = A k = π 2 × 10 c k = π 2 × 10 2 c [1] 2 2 gradient × π 2 × π 2 gradient gradient gradient Safety considerations (1 mark) S Precaution linked to mass leaving vibrating plate, e.g. use safety screen/goggles/sand tray. [1] Additional detail (4 marks) D Relevant points might include [4] 1 Wait for vibrator to oscillate evenly 2 Method to determine period of oscillation from c.r.o., i.e. one time period × time-base 3 Method to determine f from c.r.o. having determined T, i.e. f = 1 / T 4 Method to determine V from c.r.o, i.e. amplitude (height) × y-gain 5 Relationship is valid if the graph is a straight line passing through the origin [For lg – lg graph the gradient must be correct (–2 or –0.5)] 6 Determine f (allow V if consistent with above) by increasing and decreasing V or f 7 Clean surfaces of metal plate/small mass 8 Spirit level to keep plate horizontal/eye level to look for gap Do not allow vague computer methods.

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2 A student is investigating the performance of a motor vehicle. The vehicle is driven at a constant speed v on a test track, as shown in Fig. 2.1. Fig. 2.1 The performance P of the vehicle is the distance travelled per unit volume of fuel, measured in kilometres per litre (km l –1). This is obtained from the vehicle’s computer system. The experiment is repeated for different speeds. It is suggested that P and v are related by the equation P = kv m where k and m are constants. (a) A graph is plotted of lg P on the y-axis against lg v on the x-axis. Determine expressions for the gradient and y-intercept. gradient = ...................................................... y-intercept = ...................................................... [1] (b) Values of v and P are given in Fig. 2.2. v / km h–1 P / km l –1 lg (v / km h–1) lg (P / km l –1) 50 20.5 ± 0.5 61 16.0 ± 0.5 71 13.0 ± 0.5 80 11.0 ± 0.5 90 9.5 ± 0.5 99 8.0 ± 0.5 Fig. 2.2 Calculate and record values of lg (v / km h–1) and lg (P / km l –1) in Fig. 2.2. Include the absolute uncertainties in lg (P / km l –1). [3] (c) (i) Plot a graph of lg (P / km l –1) against lg (v / km h–1). Include error bars for lg (P / km l –1). [2] (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] 1.35 1.30 1.25 lg (P / km l –1) 1.20 1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 lg (v / km h–1)

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Mark Expected Answer Additional Guidance (a) A1 gradient = m y-intercept = lg k (b) T1 Allow a mixture of significant figures. T2 1.70 or 1.699 1.312 or 1.3118 T1 (first column) and T2 (second column) must be values in table. 1.79 or 1.785 1.204 or 1.2041 1.85 or 1.851 1.114 or 1.1139 1.90 or 1.903 1.041 or 1.0414 1.95 or 1.954 0.98 or 0.978 2.00 or 1.996 0.90 or 0.903 U1 From ±0.01 to ±0.03 Allow more than one significant figure. (c) (i) G1 Six points plotted correctly Must be within half a small square. Do not allow “blobs”. Ecf allowed from table. U2 Error bars in lg P plotted correctly All error bars to be plotted. Must be accurate to less than half a small square. (ii) G2 Line of best fit Upper end of line must pass between (1.75, 1.24) and (1.75, 1.255) and lower end of line must pass between (2.00, 0.900) and (2.00, 0.915). G3 Worst acceptable straight line. Line should be clearly labelled or dashed. Steepest or shallowest possible Examiner judgement on worst acceptable line that passes through all the line. Lines must cross. Mark scored only if error bars. error bars are plotted. (iii) C1 Gradient of line of best fit 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 –1.35.) U3 Uncertainty in gradient Method of determining absolute uncertainty: difference in worst gradient and gradient. (iv) C2 y-intercept Check substitution into y = mx + c. Allow ecf from (c)(iii). (Should be about 4.) Do not allow read-off of false origin. U4 Uncertainty in y-intercept Uses worst gradient and point on worst acceptable line. Do not check calculation. Do not allow if false origin used. (d) (i) C3 k = 10y-intercept C4 m = gradient and given to 2 or 3 s.f. Must be negative. and in the range –1.30 to –1.44 Allow –1.3 or –1.4 (2 s.f.) (ii) U5 Percentage uncertainty in k 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) (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) (ii) [U5] max k = 10max y-intercept and min k = 10min y-intercept 1 (max k − min k ) max k − k k − min k 2 percentage uncertainty = × 100 = × 100 = × 100 k k k

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