Cambridge A Level Physics 9702 — 2007 May/June Paper 5 · Variant 1

1 It is useful to know how the speed of an object is affected by its size when it moves through liquid in a confined space. In a laboratory this can be modelled by dropping small steel balls through oil. It is suggested that the terminal velocity v is related to the radius r of a steel ball by the equation v = kr 2 where k is a constant. Design a laboratory experiment to investigate whether v is related to r as indicated in the above equation. 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) how the radius of the steel ball would be measured, (c) how the terminal velocity of the steel ball in oil would be measured, (d) the control of variables, (e) how the data would be analysed, (f) any safety precautions that you would take. 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Mark scheme: 1 Planning (15 marks) Defining the problem (3 marks)

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2 Conducting putty is a soft material which can easily be made into different shapes. It conducts electricity. An experiment was carried out to investigate how the resistance of a fixed volume of conducting putty varied with its length. The resistance of the conducting putty was measured using an ohmmeter, as shown in Fig. 2.1. ohmmeter metal metal contact contact cylinder of conducting putty plate plate l Fig. 2.1 Examiner’s Use Values of the length l of the conducting putty and the resistance R as measured by the ohmmeter are given in Fig. 2.2. l / cm R / Ω 6.0 ± 0.4 25 10.0 ± 0.4 60 14.0 ± 0.4 115 18.0 ± 0.4 185 22.0 ± 0.4 275 26.0 ± 0.4 380 Fig. 2.2 It is suggested that the resistivity ρ of the conducting putty is given by the formula (R – R0)V ________ ρ = l2 where R0 is the resistance of the connecting wires and V is the volume of the conducting putty. (a) Explain why plotting a graph of R against l2 would enable you to confirm the relationship between R and l. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[1] (b) Calculate and record values of l2, in cm2, in the table. Include in the table the absolute errors in l2. [3] (c) (i) Plot a graph of R (y-axis) against l2 (x-axis). Include error bars for l2. [2] (ii) Draw a best-fit straight line and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the best-fit line. Include the error in your answer. gradient = ..................................... [2] Examiner’s Use 400 350 300 R/Ω 250 200 150 100 50 0 0 100 200 300 400 500 600 700 l2/cm2 Question 2 continues over the page.

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Approach to data analysis (1 mark) ρl 2 (a) R = + R 0 and a correct comment. V This mark is not scored for R being proportional to l 2. [1] Table of results (2 marks) (b) Column heading for l 2. Allow l 2 / cm2 and l 2 (cm2) (or equivalent units). [1] (b) Values of l 2. [1] 36, 100, 196, 324, 484, 676 3 significant figures needed (except 1st row). Allow 4sf. All correct for one mark. Graph (3 marks) (c) (i) Points plotted correctly. [1] All six required for this mark and must be Ğ half a small square. Indicate an error. Ecf from (b) (c) (ii) Line of best fit. [1] Must be within tolerances. Do not allow a line forced through the origin. (c) (iii) Worst acceptable straight line. [1] Must be within tolerances. Line should be clearly labelled. Allow broken line. Conclusion (4 marks) (c) (iii) gradient of best-fit line [1] Gradient should be in the range 0.550 to 0.560. If (b) and/or (c)(i) and/or (ii) are incorrect then the triangle used should be greater than half the length of the drawn line. Check the read offs and ratio to be correct. Work to half a small square. (d) Value of ρ Candidate’s gradient value = ρ/V. May be implicit from working. [1] ρ in range 10.3 -10.6 [1] (d) Unit of ρ. Must be consistent with previous answer e.g. Ω cm [1] GCE A/AS LEVEL – May/June 2007 9702 05 Treatment of errors (5 marks) (b) Errors in l 2 [1] ± 4.6 – 5.0 ± 7.8 – 8.2 ± 11.0 – 11.4 ± 14.2 - 14 or 15 ± 17 or 18 ± 20 or 21 (c) (i) error bars in l 2 plotted correctly [1] Must be within tolerances. For ecf check first and last point (c) (iii) error in gradient [1] Check method e.g. gradient of best-fit line – gradient of worst acceptable line (d) correct method for determining error in ρ (e.g. (worst gradient × volume) - ρ) [1] Value for error in ρ in the range ± 0.4 to ± 0.6. [1] Last mark is zero if vertical error bars plotted or wrong worst acceptable line plotted. [Total: 15]

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