Cambridge A Level Physics 9702 — 2016 May/June Paper 5 · Variant 2

This document consists of 8 printed pages. DC (CW/SG) 109583/2 © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level * 1 3 0 9 6 6 0 6 0 4 * PHYSICS 9702/52 Paper 5 Planning, Analysis and Evaluation May/June 2016 1 hour 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. 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 an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. Electronic calculators may be used. 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.

2 9702/52/M/J/16 © UCLES 2016 1 A student is investigating the acceleration of a trolley moving up an inclined plane as shown in Fig. 1.1. trolley inclined plane F e bench Fig. 1.1 The student is investigating the relationship between the acceleration a of the trolley and the angle θ of the inclined plane when a force F is applied to the trolley. It is suggested that the relationship is ma = F – (mg sin θ + k ) where g is the acceleration of free fall, m is the mass of the trolley and k is a constant. Design a laboratory experiment to test the relationship between a and θ. Explain how your results could be used to determine a value for k. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to • the procedure to be followed, • the measurements to be taken, • the control of variables, • the analysis of the data, • any safety precautions to be taken. [15]

3 9702/52/M/J/16 © UCLES 2016 [Turn over Diagram … … … … … … … … … … … … … … …

4 9702/52/M/J/16 © UCLES 2016 … … … … … … … … … … … … … … … … … … … … … … … … … … … [Total: 15]

5 9702/52/M/J/16 © UCLES 2016 [Turn over 2 A student is investigating how the resistance of a wire depends on the diameter of the wire. The circuit is set up as shown in Fig. 2.1. 1 ohmmeter wire Fig. 2.1 The resistance R of the wire is measured using an ohmmeter. The experiment is repeated for wires of the same material and same length L but different diameter d. It is suggested that R and d are related by the equation R = 4ρL πd 2 where ρ is a constant. (a) A graph is plotted of R on the y-axis against 1 d 2 on the x-axis. Determine an expression for the gradient. gradient = …[1]

6 9702/52/M/J/16 © UCLES 2016 (b) Values of d and R are given in Fig. 2.2. d / 10–3 m R / Ω 0.91 ± 0.01 1.6 0.56 ± 0.01 4.4 0.46 ± 0.01 6.6 0.38 ± 0.01 9.7 0.32 ± 0.01 13.9 0.27 ± 0.01 19.5 Fig. 2.2 Calculate and record values of 1 d 2 / 106 m–2 in Fig. 2.2. Include the absolute uncertainties in 1 d 2 . [3] (c) (i) Plot a graph of R / Ω against 1 d 2 / 106 m–2. Include error bars for 1 d 2 . [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 absolute uncertainty in your answer. gradient = …[2]

7 9702/52/M/J/16 © UCLES 2016 [Turn over R / 1 0 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0 2 4 6 8 10 12 14 16 18 20 1 G2 / 106 m–2

8 9702/52/M/J/16 © UCLES 2016 (d) (i) Using your answers to (a) and (c)(iii), determine the value of ρ. Include an appropriate unit. Data: L = 1.00 ± 0.01 m. ρ = …[2] (ii) Determine the percentage uncertainty in ρ. percentage uncertainty in ρ = … % [1] (e) The experiment is repeated with a thinner wire of diameter 0.23 ± 0.01 mm. The wire is of the same material and length. Determine the resistance R of the wire. Include the absolute uncertainty in your answer. R = …Ω [2] [Total: 15] To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series.

® IGCSE is the registered trademark of Cambridge International Examinations. This document consists of 6 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level PHYSICS 9702/52 Paper 5 Planning, Analysis and Evaluation May/June 2016 MARK SCHEME Maximum Mark: 30 Published 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 should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the May/June 2016 series for most Cambridge IGCSE®, Cambridge International A and AS Level components and some Cambridge O Level components.

Page 2 Mark Scheme Syllabus Paper Cambridge International AS/A Level – May/June 2016 9702 52 © Cambridge International Examinations 2016 Question 1 Planning (15 marks) Defining the problem (2 marks) P θ is the independent variable and a is the dependent variable, or vary θ and measure a. [1] P Keep F constant. [1] Methods of data collection (4 marks) M Diagram showing inclined plane with labelled support (not if a ruler used as the inclined plane or as vertical support). [1] M Method to measure angle e.g. use a protractor to measure θ or use a ruler to measure marked distances from which sin θ or θ may be determined. (Allow a labelled protractor in the correct position.) [1] M Method to measure a time or velocity to determine a, e.g. measure the time using a stopwatch, light gate(s) connected to a timer, motion sensor connected to a time display. [1] M Use a balance to measure the mass of the trolley. [1] Method of analysis (3 marks) A Plot a graph of a against sin θ. or Plot a graph of ma against sin θ. or Plot a graph of ma against mg sin θ. [1] A Relationship is valid if the graph is a straight line and does not pass through the origin [1] A k = F – m × (y-intercept) or k = F – (y-intercept) or k = F – (y-intercept) [1] Do not allow lg-lg graphs. Additional detail (6 marks) Relevant points might include: [6] 1 Keep mass of trolley constant/use same trolley. 2 Correct trigonometry relationship to determine sin θ or θ using marked lengths. 3 Use ruler to measure appropriate distance to determine a, e.g. length of slope, length of card for light gate method, position of motion sensor. 4 Equation to determine a from measurements taken appropriately with a as the subject. 5 Measurement of F for a valid method e.g. take reading from newton-meter or from stretched elastic/spring from extension (allow falling weight e.g. F = mg). 6 Use a constant extension to produce a constant force when using stretched spring/elastic.

Page 3 Mark Scheme Syllabus Paper Cambridge International AS/A Level – May/June 2016 9702 52 © Cambridge International Examinations 2016 7 Method to ensure the inclined plane is the same height each side of the plane or spirit level across plane or ensure force F (or string) is parallel to the plane. 8 Safety precaution linked to falling mass/trolley or spring/elastic breaking (not string). 9 Rearrangement of relationship into y = mx + c e.g. ma = –mg sin θ + (F – k) or m k F g a − + − = θ sin or correct y-intercept (subject must be y-axis). 10 Repeat experiment for each angle θ to find average for a. Do not allow vague computer methods.

Page 4 Mark Scheme Syllabus Paper Cambridge International AS/A Level – May/June 2016 9702 52 © Cambridge International Examinations 2016 Question 2 Analysis, conclusions and evaluation (15 marks) Mark Expected Answer Additional Guidance (a) A1 ρ π 4 L (b) T1 2 1 d / 106 m–2 T2 1.2 or 1.21 3.2 or 3.19 4.7 or 4.73 6.9 or 6.93 9.8 or 9.77 14 or 13.7 All values to 2 s.f. or 3 s.f. Allow a mixture of significant figures. Must be values in table. U1 From ± 0.03 to ± 1 Allow more than one significant figure. Allow zero for first uncertainty and up to 1.2 for largest uncertainty. (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 2 1 d plotted correctly All error bars to be plotted. Length of bar must be accurate to less than half a small square and symmetrical. (ii) G2 Line of best fit Lower end of line must pass between (2.6, 4.0) and (3.0, 4.0) and upper end of line must pass between (12.4, 18.0) and (13.0, 18.0). G3 Worst acceptable straight line. Steepest or shallowest possible line that passes through all the error bars. Line should be clearly labelled or dashed. Examiner judgement on worst acceptable line. Must be steepest/shallowest line. Mark scored only if 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 1.4 –1.5 × 10–6.) U3 Absolute uncertainty in gradient Method of determining absolute uncertainty: difference in worst gradient and gradient.

Page 5 Mark Scheme Syllabus Paper Cambridge International AS/A Level – May/June 2016 9702 52 © Cambridge International Examinations 2016 Mark Expected Answer Additional Guidance (d) (i) C2 π× = × gradient 0.7854 gradient 4L Must use gradient value. Do not penalise POT (Should be about 1 × 10–6.) C3 Ω m Correct unit and correct power of ten. (ii) U4 Percentage uncertainty in ρ Percentage uncertainty in gradient + 1%. (e) C4 R in the range 25.5 to 28.4 and given to 2 or 3 s.f. Allow 26 or 27 or 28. Allow ECF for POT error in (d)(i) e.g. 2.7 × 107. U5 Absolute uncertainty in R Percentage uncertainty must be greater than 8.6%.

Page 6 Mark Scheme Syllabus Paper Cambridge International AS/A Level – May/June 2016 9702 52 © Cambridge International Examinations 2016 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]     ∆ ∆ = + × = × +         gradient 0.01 gradient percentage uncertainty 100 100 1% gradient 1.00 gradient ρ π× π× = = × × max gradient max gradient max 4 min 4 0.99 L ρ π× π× = = × × min gradient min gradient min 4 max 4 1.01 L (e) [U5]     ∆ ∆   = + × × = + ×             gradient 0.01 gradient percentage uncertainty 2 100 0.086 100 gradient 0.23 gradient ρ ρ ρ ρ     ∆ ∆   = + + × × = + ×             0.01 0.01 percentage uncertainty 2 100 0.096 100 1.00 0.23 = 2 min max gradient maxR d ρ × × = π× max max 2 min 4 max L R d = 2 max min gradient minR d ρ × × = π× min min 2 max 4 min L R d