Cambridge A Level Physics 9702 — 2014 Oct/Nov Paper 5 · Variant 1

1 A student investigates the power dissipated by a lamp connected to a model wind turbine as shown in Fig. 1.1. wind turbine lamp Fig. 1.1 The power P dissipated in the lamp depends on the angle θ between the axis of the turbine and the direction of the wind, as shown by the top view in Fig. 1.2. turbine wind direction e Fig. 1.2 It is suggested that P = k cosθ where k is a constant. Design a laboratory experiment to test the relationship between P and θ and 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 (cos) θ is the independent variable, or vary (cos) θ. [1] P P is the dependent variable, or measure P. [1] P Keep the speed of the air constant. Allow keep power to the fan/hairdryer constant. [1] Methods of data collection (5 marks) M Labelled diagram showing method to produce air flow in line with turbine. Method of producing “wind” must be labelled. [1] M Circuit connecting turbine to lamp with ammeter and voltmeter connected correctly. No additional power supplies in the lamp circuit. [1] M P = IV. Do not allow I2R or V2/R unless it is clear that R is determined from V / I. Allow wattmeter or joule meter and stopwatch. [1] M Measure angle with protractor or use rule to measure appropriate distances. [1] M Ensure that there are no other draughts or airflows. [1] Method of analysis (2 marks) A Plot a graph of P against cos θ. [1] A k = gradient. [1] Safety considerations (1 mark) S Precaution linked to avoiding air flow entering eyes or avoid moving blades. [1] Additional detail (4 marks) D Relevant points might include [4] 1 Use of large wind speed to gain measurable readings. 2 Use of low wattage/low resistance lamp or turbine with low friction. 3 Additional detail on measuring (cos) θ – correct angle must be determined. 4 Wait until airflow/turbine/meter readings constant. 5 Avoid turbulence or reflection of air flow. 6 Ensure distance from fan to turbine is constant. 7 Relationship is valid if the graph is a straight line passing through the origin. 8 Method to check that wind speed is constant. Do not allow vague computer methods. [Total: 15]

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2 A student investigates electrical resonance in a circuit containing a capacitor and a coil connected in parallel. The circuit is set up as shown in Fig. 2.1. signal generator A coil C Fig. 2.1 The resonant frequency f is the frequency at which the current measured by the ammeter is a minimum. An experiment is carried out to investigate how f varies with the capacitance C of the capacitor. It is suggested that f and C are related by the equation 1 f = 2π LC where L is a constant for the circuit. 2 1 (a) A graph is plotted of f on the y-axis against on the x-axis. Determine an expression C for the gradient in terms of L. gradient = ................................................. [1] (b) Values of f and C are given in Fig. 2.2. 1 C / 10–4 F f / Hz / 103 F–1 f 2 / 103 Hz2 C 2.5 ± 10% 149 3.0 ± 10% 134 3.5 ± 10% 123 4.4 ± 10% 107 6.6 ± 10% 82 8.8 ± 10% 65 Fig. 2.2 1 2 Calculate and record values of / 103 F–1 and f / 103 Hz2 in Fig. 2.2. C 1 Include the absolute uncertainties in . [3] C 2 1 1(c) (i) Plot a graph of f / 103 Hz2 against / 103 F–1. Include error bars for . [2] C C (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] 24 22 f 2 / 103 Hz2 20 18 16 14 12 10 8 6 4 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 1 — / 103 F–1 C

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Mark Expected Answer Additional Guidance (a) A1 1 gradient = 2 4 π L (b) T1 T1 (first column) and T2 (second column) T2 4.0 or 4.00 22.2 or 22.20 must be table values. Allow a mixture of significant figures. 3.3 or 3.33 18.0 or 17.96 2.9 or 2.86 15.1 or 15.13 2.3 or 2.27 11.4 or 11.45 1.5 or 1.52 6.7 or 6.72 1.1 or 1.14 4.2 or 4.23 U1 From ± 0.4 (or ± 0.5) to ± 0.1 Allow more than one significant figure. (or ± 0.2) (c) (i) G1 Six points plotted correctly Must be within half a small square. Penalise “blobs”. Ecf allowed from table. U2 Error bars in 1/C plotted correctly All error bars to be plotted. Must be accurate to less than half a small square. (c) (ii) G2 Line of best fit If points are plotted correctly then lower end of line should pass between (1.65, 8.0) and (1.75, 8.0) and upper end of line should pass between (3.95, 22) and (4.05, 22). Allow ecf from points plotted incorrectly – examiner judgement. 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. all error bars are plotted. (c) (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. (Should be about 6.) U3 Uncertainty in gradient correctly Method of determining absolute determined uncertainty: difference in worst gradient and gradient. (d) C2 1 Allow ecf from (c)(iii). L = 2 (Should be about 4 × 10–3.) 4 π × gradient C3 F–1 Hz–2 or s2 F–1 Allow H or kg m2 A–2 s–2 or Ω Hz–1 or Ω s. Conventional notation required. U4 Absolute uncertainty in L. (e) (i) C4 f in the range 760 to 800 and 1 gradient given to 2 or 3 s.f. f = = 2 π LC C (ii) U5 Percentage uncertainty in f. ½(Percentage uncertainty in L + Must be greater than 5%. percentage uncertainty in C) [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) (d) [U4]  ∆gradient  absolute uncertainty in L =  × L   gradient  1 max L = 2 4 π × min gradient 1 min L = 4 π 2 × max gradient (e) (ii) [U5] 1  ∆L  1  ∆gradient  % uncertainty =  × 100 + 10  =  × 100 + 10  2  L  2  gradient  1 max gradient max f = = 2 π LminCmin min C 1 min gradient min f = = 2 π Lmax Cmax max C

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