Cambridge A Level Physics 9702 — 2015 Oct/Nov Paper 5 · Variant 2

1 A student is investigating the angle at which a glass cylinder containing oil topples, as shown in Fig. 1.1. q glass cylinder oil bench Fig. 1.1 A cylinder containing a mass m of oil can be tilted through a maximum angle φ from the vertical before it topples. It is suggested that the relationship between m and φ is 1 am = + b tan φ ρd 3 where d is the diameter of the cylinder, ρ is the density of the oil and a and b are constants. Design a laboratory experiment to test the relationship between φ and m. Explain how your results could be used to determine values for a and b. 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 m is the independent variable, or vary m. [1] P (tan)φ is the dependent variable, or measure (tan) φ. [1] P Keep the temperature of the oil constant. [1] Methods of data collection (5 marks) M Labelled diagram showing labelled protractor positioned to determine φ for tilted cylinder. Allow distances marked to determine φ and use of a rule. [1] M Use of balance/scales to measure the mass of the oil/cylinder. [1] M Mass of oil = mass of (oil + cylinder) – mass of cylinder. [1] M Use of vernier calipers/micrometer/rule to measure d. [1] M Repeat each experiment for the same value of m and average φ. [1] Method of analysis (2 marks) 1 A Plot a graph of against m. tan φ m m m or (Allow d 3 ρ d 3 or ρ . Do not allow log-log graphs.) [1] A a = gradient ×ρd3 and b = y-intercept; must be consistent with suggested graph. [1] Safety considerations (1 mark) S Precaution linked to preventing spilling oil, e.g. use a tray/lid/cloth to absorb oil (do not allow just wiping or mopping) or precaution linked to preventing glass cylinder breaking, e.g. padding/cushion or use of gloves to prevent skin irritation (do not allow “because oil is slippery”). [1] Additional detail (4 marks) D Relevant points might include [4] 1 Repeat measurements of d in different directions and average 2 Use of video with slow motion/frame by frame playback to determine φ 3 Use large protractor to reduce percentage uncertainty or trigonometry relationship related to measurements to be taken 4 Use the same (diameter) cylinder (not “same size” but allow “same size and shape”) 5 Slowly/gently/gradually tilt cylinder of oil/use of rough surface (to prevent sliding) 6 Experimental method to determine density of oil and ρ = m / V 7 Relationship is valid if the graph is a straight line that does NOT pass through the origin / has an intercept; must be consistent with suggested graph Do not allow vague computer methods.

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2 A student is investigating an electrical circuit containing a length of nichrome wire. The circuit is set up as shown in Fig. 2.1. E A I L nichrome wire Fig. 2.1 The length L of the wire in the circuit is varied and the current I is measured. It is suggested that I and L are related by the equation 1 4ρL r = + I πEd 2 E where E is the e.m.f. of the battery, d is the diameter of the wire and ρ and r are constants. 1 (a) A graph is plotted of on the y-axis against L on the x-axis. I Determine expressions for the gradient and y-intercept. gradient = ...................................................... y-intercept = ...................................................... [1] (b) Values of L and I are given in Fig. 2.2. L / 10–2 m I / A 40.0 0.24 ± 0.01 48.0 0.20 ± 0.01 60.0 0.17 ± 0.01 70.0 0.15 ± 0.01 80.0 0.13 ± 0.01 92.0 0.12 ± 0.01 Fig. 2.2 1 Calculate and record values of / A–1 in Fig. 2.2. I 1 Include the absolute uncertainties in / A–1. [3] I 1(c) (i) Plot a graph of / A–1 against L / 10–2 m. I 1 Include error bars for / A–1. [2] I (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 absolute uncertainty in your answer. gradient = ................................................. [2] 1 / $²I

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Mark Expected Answer Additional Guidance (a) A1 4 ρ gradient = 2 πEd r y-intercept = E (b) T1 1 1 1  1  / A–1 Allow (A–1) or   . I I I  A  T2 Allow a mixture of significant figures. 4.2 or 4.17 Must be table values. 5.0 or 5.00 5.9 or 5.88 6.7 or 6.67 7.7 or 7.69 8.3 or 8.33 U1 ± 0.2 to ± 0.6 or ± 0.7 or ± 0.8 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 1 / I plotted All error bars to be plotted. Must be accurate to correctly less than half a small square. Length of bar must be accurate to less than half a small square. Do not allow less than 0.05. (ii) G2 Line of best fit If points are plotted correctly then lower end of line should pass between (41, 4.5) and (44, 4.5) and upper end of line should pass between (83, 8.0) and (88, 8.0). Line should not go from bottom to top points. G3 Worst acceptable straight line. Line should be clearly labelled or dashed. Steepest or shallowest Examiner judgement on worst acceptable line. possible line that passes Lines must cross. Mark scored only if error bars through all the error bars. are plotted. (iii) C1 Gradient of line of best fit 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 8.) U3 Absolute uncertainty in Method of determining absolute uncertainty: gradient difference in worst gradient and gradient. (iv) C2 y-intercept Check substitution into y = mx + c. Allow ECF from (c)(iii). (Should be about 0.7–1.5.) U4 Absolute uncertainty in y- Uses worst gradient and point on WAL. intercept Do not check calculation. (d) (i) C3 ρ = 2.415 × 10–7 × gradient Must use gradient. πEd 2 ρ = × gradient Must be in the range 4 1.80 × 10–6 to 2.10 × 10–6 and [2 × 10–6 Ω m = 2 × 10–4 Ω cm = 2 × 10–3 Ω mm] given to 2 or 3 s.f. C4 r = E × y-intercept Must include units for ρ and r. = 3.2 × y-intercept Allow V A–1 or kg m2 A–2 s–3 for Ω. and Ω m and Ω given (ii) U5 Percentage uncertainty in ρ Must be greater than 9.6%. 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]  ∆m 0.1 0.01  percentage uncertainty =  + + 2 ×  × 100  m 3.2 0.31   ∆m  =  × 100  + 3.125 + 2 × 3.226  m  − 3 2 π × 3.3 × (0.32 × 10 ) max. p = × max. gradient 4 − 3 2 π × 3.1 × (0.30 × 10 ) min. p = × min. gradient 4

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