Cambridge A Level Physics 9702 — 2009 May/June Paper 5 · Variant 1

1 A student wishes to determine the Young modulus E of wood from the period of oscillation of For a loaded wooden rule, as shown in Fig. 1.1. Examiner’s Use fixed end load l Fig. 1.1 An equation relating the period of oscillation T to the overhanging length l of the rule is kl 3 T 2 = . E The constant k is given by 16π 2M k = wd 3 where M is the mass of the load, w is the width of the rule and d is the thickness of the rule. Design a laboratory experiment to determine the Young modulus of wood. You should draw a diagram 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) how to analyse the data, (e) how to determine E, (f) the safety precautions to be taken. [15] Diagram For Examiner’s Use ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ For ........................................................................................................................................................ Examiner’s Use ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mark scheme: 1 Planning (15 marks) Defining the problem (3 marks) P1 Vary l or l is the independent variable [Allow M] [1] P2 Determine the period T (for each l [M]) or T is the dependent variable [1] P3 M is kept constant [l is kept constant] [1] Methods of data collection (5 marks) M1 Diagram showing the cantilever is fixed e.g. g-clamp & bench, retort stand & clamp [1] M2 Many oscillations repeated to determine average T (n [ 10 or t [ 10 s for stopwatch) [1] M3 Weigh M using balance [1] M4 Measure w and d and measure/record l [1] M5 Use of vernier caliper/micrometer to measure d and/or w [1] Method of analysis (2 marks) A1 Appropriate graph plotted i.e. T 2 against l 3; [T 2 against M] or lg T against lg l or lg M [1] 16π 2 M k 16 π 23l A2 E = 3 = E = 3 wd × gradient gradient wd × gradient k k Allow logarithmic solutions e.g. E = 2 xy - intercept = y - intercept [1] 10 100 Safety considerations (1 mark) S1 Relevant safety precaution related to the use of loads [1] e.g. cushion/sand in case load falls, keep feet away, keep distance from experiment. Additional detail (4 marks) D Relevant points might include [4] 1. Use same rule or keep w and/or d constant. 2. Repeat measurements of d and/or w along rule and average. 3. Discussion of use of motion sensor e.g. orientation or light gates with detail. 4. Use small amplitude or small angle oscillations (to ensure equation is valid). 5. Method of securing load to rule e.g. with tape/glue. 6. Discussion of magnitude of load: large enough to make T large enough. 7. Use of fiducial marker to help to time. 8. Start timing after oscillations have settled. Do not allow vague use of computers/light gates, video cameras, dataloggers. [Total: 15] GCE A/AS LEVEL – May/June 2009 9702 05

More questions on Stress and strain

2 An experiment is carried out to investigate how the current I required to melt a wire varies For with the diameter d of the wire. Examiner’s Use The equipment is set up as shown in Fig. 2.1. A wire Fig. 2.1 Question 2 continues on the next page. It is suggested that I and d are related by the equation For Examiner’s Use I = pd q where p and q are constants. (a) A graph is plotted with lg I on the y-axis and lg d on the x-axis. Express the gradient and y-intercept in terms of p and q. gradient = ………………………………… y-intercept = ………………………………… [1] (b) Values of d and I are given in Fig. 2.2. d / 10–5 m I / A lg (d / 10–5 m) lg (I / A) 15 2.6 ± 0.1 19 3.5 ± 0.1 23 4.4 ± 0.1 27 5.4 ± 0.1 31 6.4 ± 0.1 Fig. 2.2 Calculate and record values of lg (d / 10–5 m) and lg (I / A) in Fig. 2.2. Include in the table the absolute errors in lg (I / A). [3] (c) (i) Plot a graph of lg (I / A) against lg (d / 10–5 m). Include error bars for lg (I/ A). [2] (ii) Draw the 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 error in your answer. gradient = ………………………………… [2] 0.85 For Examiner’s Use 0.80 lg (I / A) 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 lg (d / 10-5 m)

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Part Mark Expected Answer Additional Guidance (a) A1 gradient = q y-intercept = lg p or log p (b) T1 1.176 or 1.18 0.415 or 0.41 T1 is awarded for correct values lg d T2 1.279 or 1.28 0.544 or 0.54 T2 is awarded for correct values lg I 1.362 or 1.36 0.643 or 0.64 A mixture of 2dp and 3dp is allowed within 1.431 or 1.43 0.732 or 0.73 each column 1.491 or 1.49 0.806 or 0.81 E1 ± 0.016 or ± 0.017 or ± 0.02 Allow more than one significant figures. decreasing to ± 0.006 or ± 0.007 or ± 0.01 (c) (i) G1 Five points plotted correctly Must be within half a small square. Use transparency. Ecf allowed from table. E2 Error bars in lg I plotted correctly. Check first and last point. Must be accurate within half a small square. Ecf allowed from table. (ii) G2 Line of best fit If points are plotted correctly then lower end of line should pass between (1.15, 0.370) and (1.15, 0.385) and upper end of line should pass between (1.50, 0.815) and (1.50, 0.825). Allow ecf from points plotted incorrectly – examiner judgement. G3 Worst acceptable straight line. Line should be clearly labelled or dashed. Steepest or shallowest possible Should pass from top of top error bar to line that passes through all the bottom of bottom error bar or bottom of top error bars. error bar to top of bottom error bar. Mark scored only if error bars are plotted. (iii) C1 Gradient of best fit line The triangle used should be greater than half the length of the drawn line. Check the “read offs”. Work to half a small square. Do not penalise POT. E3 Error in gradient Method of determining absolute error Difference in worst gradient and gradient. (iv) C2 y-intercept Must be negative and the gradient must be used. Check substitution into c = y – mx. Allow ecf from (c)(iii). If gradient within range given, then y-intercept should be about –1.1 E4 Method of determining error in Determines worst y-intercept using worst y-intercept gradient and finds difference. Check substitution but do not check calculation. Do not allow ecf from false origin read-off. GCE A/AS LEVEL – May/June 2009 9702 05 (d) C3 p = 10candidate’s y-intercept p should be about 0.08. Allow ecf from (c)(iv). If FO used then p should be about 2.34 to 2.43. C4 q = in the range 1.20–1.30 and Candidate’s gradient must be used. given to 2 or 3 sf. E5 Method for determining errors in Determines worst p using worst y-intercept values of p and q. and finds difference. Allow ecf from (c)(iv). q error must be same as error in gradient. [Total: 15] Uncertainties in Question 2 (c) (iii) Uncertainty in gradient [E3] 1. Uncertainty = gradient of line of best fit – gradient of worst acceptable line 2. Uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (c) (iv) Uncertainty in the y-intercept [E4] 1. Uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line 2. Uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept) N.B. Must use gradient from worst acceptable line and a point on the same worst acceptable line to determine y-intercept of worst acceptable line. (d) Uncertainty in p [E5] 1. Uncertainty = p from y-intercept of BFL – p from y-intercept of WAL 2. Uncertainty = ½ (p from y-intercept of shallowest WAL – p from y-intercept of steepest WAL)

More questions on Potential difference and power