Cambridge A Level Physics 9702 — 2012 May/June Paper 5 · Variant 2

This document consists of 8 printed pages. DC (KN/SW) 42263/3 © 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 9702/52 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 * 8 2 5 6 4 9 4 0 3 7 *

2 9702/52/M/J/12 © UCLES 2012 For Examiner’s Use 1 A hot air balloon is tied to the ground using a rope. As the wind blows with speed v, the rope makes an angle θ to the horizontal, as shown in Fig 1.1. θ rope wind with speed v ground Fig 1.1 It is suggested that tan θ is inversely proportional to v 2. To model the hot air balloon in the laboratory, a balloon filled with helium is used. Design a laboratory experiment using a small helium-filled balloon to test the relationship between θ and v. 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 9702/52/M/J/12 © UCLES 2012 [Turn over For Examiner’s Use Diagram … … … … … … … … … … … … … … …

4 9702/52/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 9702/52/M/J/12 © UCLES 2012 [Turn over For Examiner’s Use 2 A student investigates how the resonant length L of a loaded wire varies with frequency f. 30 N wire signal generator L Fig. 2.1 For six different frequencies, the student records the length L. Question 2 continues on the next page.

6 9702/52/M/J/12 © UCLES 2012 For Examiner’s Use It is suggested that f and L are related by the equation f = 1 2L T μ where T is the tension in the wire and μ is a constant. (a) A graph is plotted of f on the y-axis against 1 / L on the x-axis. Determine an expression for the gradient in terms of T and μ. gradient = … [1] (b) Values of f and L are given in Fig. 2.2. f / Hz L / 10–2 m 256 54.5 ± 0.5 294 48.0 ± 0.5 330 42.5 ± 0.5 350 40.0 ± 0.5 396 35.5 ± 0.5 440 32.0 ± 0.5 Fig. 2.2 Calculate and record values of (1 / L) / m–1 in Fig. 2.2. Include the absolute uncertainties in 1 / L. [3] (c) (i) Plot a graph of f / Hz against (1 / L) / m–1. Include error bars for 1 / L. [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 9702/52/M/J/12 © UCLES 2012 [Turn over For Examiner’s Use 1.8 250 270 290 310 330 350 370 390 410 430 450 2.0 2.2 2.4 2.6 2.8 3.0 (1 / L) / m–1 f / Hz 3.2

8 9702/52/M/J/12 © UCLES 2012 For Examiner’s Use (d) (i) The tension T in the wire is 30 ± 3 N. Using your answer to (c)(iii), determine the value of μ. Include an appropriate unit in your answer. μ = … [2] (ii) Determine the percentage uncertainty in μ. percentage uncertainty = …% [1] (e) An expression for μ is μ = ρ π r 2 where the density ρ of the wire is 8800 kg m–3 and r is the radius of the wire. (i) Using your answer to (d)(i), determine a value for r. r = …m [1] (ii) Determine the percentage uncertainty in your value of r. percentage uncertainty = …% [1] 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 9702/52 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 52 © University of Cambridge International Examinations 2012 1 Planning (15 marks) Defining the problem (3 marks) P1 v is the independent variable and θ is the dependent variable or vary v and measure θ. [1] P2 Keep the (shape and) size/volume/surface area/mass of balloon/helium constant [1] Do not credit ‘same balloon’. P3 Keep the temperature (air/helium/balloon) constant. [1] Methods of data collection (5 marks) M1 Labelled diagram of apparatus: balloon, string fixed and method of producing wind. Method of producing wind to be approximately horizontal to balloon. [1] M2 Suspend mass from balloon. [1] M3 Method to change wind speed, e.g. change setting, variable power supply/resistor/change distance from fan. [1] M4 Method to measure wind speed, e.g. wind speed indicator/detector, anemometer [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 tan θ against 1/v2. [1] A2 Relationship valid if straight line through origin [1] Safety considerations (1 mark) S1 Avoid the moving blades of the fan (safety screen, switch off when changing experiment); goggles to avoid air stream into eye. [1] Additional detail (4 marks) D1/2/3/4 Relevant points might include [4] 1 Large wind speed to produce measurable deflection/large cross-sectional area of balloon. 2 Additional detail on measuring angle e.g. use a large protractor, projection method. 3 tan θ = h/l. 4 Measuring air speed at point where balloon is positioned. 5 Adjust height of fan so that air flow is horizontally aligned to the balloon. 6 Reason for adding mass to increase stability/deflection. 7 Keep windows shut/air conditioning switched off/use of wind tunnel to avoid draughts. 8 Wait for the balloon 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 52 © University of Cambridge International Examinations 2012 2 Analysis, conclusions and evaluation (15 marks) Part Mark Expected Answer Additional Guidance (a) A1 Gradient = µ T 2 1 Allow equivalent, e.g. µ 4 T (b) T1 1/L / m–1 or (1/L) / m–1 Allow 1/L (m–1), 1/L / 1/m, 1/L (1/m) T2 1.83 or 1.835 2.08 or 2.083 2.35 or 2.353 2.50 or 2.500 2.82 or 2.817 3.13 or 3.125 Values must correspond to table. A mixture of 3 s.f. and 4 s.f. is allowed U1 From ± 0.01 or ± 0.02, to ± 0.05 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 All Error bars in 1/L/m–1 plotted correctly. Check second and last point for accuracy. 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 (1.8, 250) and (1.8, 254) and upper end of line should pass between (3.18, 450) and (3.2, 448). 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 left of top error bar to right of bottom error bar or right of top error bar to left of bottom error bar. Mark scored only if all 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 140) U3 Uncertainty in gradient Method of determining absolute uncertainty Difference in worst gradient and gradient. (d) (i) C2 Value of µ using gradient µ = 7.5/gradient2 Gradient must be used. (Should be about 0.00037 or 3.7 × 10–4) C3 kg m–1 or N Hz–2 m–2 Allow other correct units e.g. N s2 m–2 or Pa s2 or N (Hz m)–2 (ii) U4 10% + 2 × percentage uncertainty in gradient Check working. Must be larger than 10%.

Page 4 Mark Scheme: Teachers’ version Syllabus Paper GCE AS/A LEVEL – May/June 2012 9702 52 © University of Cambridge International Examinations 2012 (e) C4 r given to 2 or 3 s.f. and in the range 1.15 × 10–4 to 1.18 × 10–4 Allow 1.2 to 2 s.f. Penalise 1 s.f. or >3 s.f. U5 (d)(ii) / 2 Check working if not (d)(ii) / 2 [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) (ii) [U4] Percentage uncertainty = 10 + 2 m m ∆ Percentage uncertainty = 100 min 4 max 2 × − × µ µ m T Percentage uncertainty = 100 max 4 min 2 × − × µ µ m T (e) (ii) [U5] Percentage uncertainty = 100 max × − r r r Percentage uncertainty = 100 min × − r r r