Cambridge A Level Physics 9702 — 2012 May/June Paper 5 · Variant 1

This document consists of 8 printed pages. DC (KN/SW) 42262/1 © UCLES 2012 [Turn over UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. You may lose marks if you do not show your working or if you do not use appropriate units. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. PHYSICS 9702/51 Paper 5 Planning, Analysis and Evaluation May/June 2012 1 hour 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. For Examiner’s Use 1 2 Total * 9 1 5 4 6 8 2 3 6 1 *

2 9702/51/M/J/12 © UCLES 2012 For Examiner’s Use 1 A fairground ride carries passengers in chairs which are attached by metal rods to a rotating central pole, as shown in Fig 1.1. When the pole rotates with angular velocity ω, the rods make an angle θ to the vertical. θ ω rotating pole metal rod Fig 1.1 It is suggested that cos θ is inversely proportional to ω2. Design a laboratory experiment, using a small object to represent an occupied chair, to test the relationship between θ and ω. 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. [15]

3 9702/51/M/J/12 © UCLES 2012 [Turn over For Examiner’s Use Diagram … … … … … … … … … … … … … … …

4 9702/51/M/J/12 © UCLES 2012 For Examiner’s Use … … … … … … … … … … … … … … … … … … … … … … … … For Examiner’s Use Defining the problem Methods of data collection Method of analysis Safety considerations Additional detail

5 9702/51/M/J/12 © UCLES 2012 [Turn over For Examiner’s Use 2 A current-carrying wire is clamped at each end, as shown in Fig 2.1. A student investigates how the deflection y at the centre of the wire varies with the current I. I to circuit to circuit y Fig. 2.1 For different currents, the deflection is recorded. Question 2 continues on the next page.

6 9702/51/M/J/12 © UCLES 2012 For Examiner’s Use It is suggested that y and I are related by the equation y = sI r where r and s are constants. (a) A graph is plotted of lg y on the y-axis against lg I on the x-axis. Determine expressions for the gradient and y-intercept in terms of r and s. gradient = … y-intercept = … [1] (b) Values of I and y are given in Fig. 2.2. I / 10–2 A y / mm lg (I / 10–2 A) lg (y / mm) 50 2.6 ± 0.2 60 3.4 ± 0.2 70 4.4 ± 0.2 80 5.4 ± 0.2 90 6.6 ± 0.2 95 7.2 ± 0.2 Fig. 2.2 Calculate and record values of lg (I / 10–2 A) and lg (y / mm) in Fig. 2.2. Include the absolute uncertainties in lg (y / mm). [3] (c) (i) Plot a graph of lg (y / mm) against lg (I / 10–2 A). Include error bars for lg (y / mm). [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]

7 9702/51/M/J/12 © UCLES 2012 [Turn over For Examiner’s Use 1.65 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 1.70 1.75 1.80 1.85 1.90 1.95 lg (I / 10–2A) lg (y / mm) 2.00

8 9702/51/M/J/12 © UCLES 2012 For Examiner’s Use (iv) Determine the y-intercept of the line of best fit. Include the uncertainty in your answer. y-intercept = … [2] (d) Using your answers to (c)(iii) and (c)(iv), determine values for r and s. Include the uncertainties in your answers. You need not be concerned with the units of r and s. r = … s = … [3] Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 9702 PHYSICS 9702/51 Paper 5 (Planning, Analysis and Evaluation), maximum raw mark 30 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes must be read in conjunction with the question papers and the report on the examination. • Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the May/June 2012 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page 2 Mark Scheme: Teachers’ version Syllabus Paper GCE AS/A LEVEL – May/June 2012 9702 51 © University of Cambridge International Examinations 2012 1 Planning (15 marks) Defining the problem (3 marks) P1 Frequency or period of rotation or ω is the independent variable and θ is the dependent variable or vary f or T or ω and measure θ. [1] P2 ω = 2πf = 2π/T [1] P3 Keep the length of the rigid rod constant; ignore reference to mass. [1] Methods of data collection (5 marks) M1 Labelled diagram of apparatus: small object, pole attached to a rotating device (motor, turntable). [1] M2 Method to change the speed of the rotating device. [1] M3 Method to determine frequency or time period (e.g. stop watch to time a number of rotations, rev counter/tachometer, light gates connected to a timer/frequency meter). [1] M4 Use fiducial mark or light gates perpendicular to motion of object. [1] M5 Method to measure angle – use protractor or rule for measurements for trigonometry methods. This must be shown correctly on diagram or explained in text. [1] Method of analysis (2 marks) A1 Plot a graph of cos θ against 1/ω 2. [1] A2 Relationship is valid if straight line through the origin [1] Safety considerations (1 mark) S1 Use a protective screen in case mass detaches from the pole. Do not use goggles. [1] Additional detail (4 marks) Relevant points might include [4] 1 Large motor speed to produce measurable θ. 2 Additional detail on measuring angle e.g. large protractor fixed to pole. 3 Projection method, slow motion freeze frame video, camera with detail. 4 cos θ = h/l or equivalent. 5 Method of checking pole is vertical – use a set square. 6 Additional detail on measuring angular velocity, e.g. time at least 10 rotations. 7 Wait for motion to become stable. Do not allow vague computer methods. [Total: 15]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper GCE AS/A LEVEL – May/June 2012 9702 51 © University of Cambridge International Examinations 2012 2 Analysis, conclusions and evaluation (15 marks) Part Mark Expected Answer Additional Guidance (a) A1 Gradient = r y-intercept = lg s Allow log or ln (b) T1 T2 1.70 or 1.699 0.41 or 0.415 1.78 or 1.778 0.53 or 0.531 1.85 or 1.845 0.64 or 0.643 1.90 or 1.903 0.73 or 0.732 1.95 or 1.954 0.82 or 0.820 1.98 or 1.978 0.86 or 0.857 Ignore significant figures. A mixture is allowed. U1 From ± 0.03 or ± 0.04, to ± 0.01 (±0.012) Allow more than one significant figure. (c) (i) G1 Six points plotted correctly Must be within half a small square. Penalise ‘blobs’ (more than half a small square). Ecf allowed from table. U2 Error bars in lg (y / mm) plotted correctly. Must be accurate within half a small square. (ii) G2 Line of best fit If points are plotted correctly then lower end of line should pass between (1.655, 0.35) and (1.665, 0.35) and upper end of line should pass between (2.00, 0.89) and (2.00, 0.90). Allow ecf from points plotted incorrectly – examiner judgement. G3 Worst acceptable straight line. Steepest or shallowest possible line that passes through all the error bars. Line should be clearly labelled or dashed. Should pass from top of top error bar to bottom of bottom error bar or bottom of top 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 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 1.6) U3 Uncertainty in gradient Method of determining absolute uncertainty. Difference in worst gradient and gradient. (iv) C2 Negative y-intercept Must be negative. FOX does not score. Expect to see point substituted into y = mx + c Allow ecf from (c)(iii) U4 Uncertainty in y-intercept Uses worst gradient and point on WAL. Do not check calculation. FOX does not score.

Page 4 Mark Scheme: Teachers’ version Syllabus Paper GCE AS/A LEVEL – May/June 2012 9702 51 © University of Cambridge International Examinations 2012 (d) C3 r = gradient and is given to 2 or 3 s.f. and in the range 1.57 to 1.64 Allow 1.6 to 2 s.f. Penalise 1 s.f. or >3 s.f. C4 s = 10y-intercept y-intercept must be used. (Should be about 0.005 or 5 × 10–3) Allow ecf for method from (c)(iv). U5 Absolute uncertainty in r and s Uncertainty in r should be the same as the uncertainty in the gradient. Difference in worst s and s. [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) (iv) [U4] Uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line Uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) (d) [U5] Uncertainty = best s –worst s