Cambridge A Level Physics 9702 — 2016 Oct/Nov Paper 5 · Variant 1

This document consists of 8 printed pages. DC (LEG/JG) 117176/2 © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level * 5 9 1 7 9 0 5 2 0 8 * PHYSICS 9702/51 Paper 5 Planning, Analysis and Evaluation October/November 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 9702/51/O/N/16 © UCLES 2016 1 A student is investigating the motion of magnets falling through a vertical copper pipe as shown in Fig. 1.1. falling magnet copper pipe Fig. 1.1 The student releases a magnet above the copper pipe. The magnet has speed v as it leaves the pipe. It is suggested that the relationship between v and B is v = v0e–λB where B is the magnetic flux density at the poles of the magnet and v0 and λ are constants. Design a laboratory experiment to test the relationship between v and B. Explain how your results could be used to determine values of v0 and λ. 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 9702/51/O/N/16 © UCLES 2016 [Turn over Diagram … … … … … … … … … … … … … …

4 9702/51/O/N/16 © UCLES 2016 … … … … … … … … … … … … … … … … … … … … … … … … … … … [Total: 15]

5 9702/51/O/N/16 © UCLES 2016 [Turn over 2 A student is investigating a circuit containing capacitors. The capacitors are initially uncharged. A capacitor of capacitance Y is charged by connecting it to a power supply. The charge is then shared with another capacitor of capacitance C connected between the terminals P and Q, as shown in Fig. 2.1. V E P Q Y C Fig. 2.1 A voltmeter is used to measure the maximum potential difference V between P and Q. The experiment is repeated by adding additional capacitors, each of capacitance C, in series between P and Q. The total capacitance X between P and Q may be determined by the equation X = C n where n is the number of capacitors in series. It is suggested that V and X are related by the equation YE = (X + Y )V where E is the e.m.f. of the power supply. (a) A graph is plotted of 1 V on the y-axis against X on the x-axis. Determine expressions for the gradient and y-intercept. gradient = … y-intercept = … [1]

6 9702/51/O/N/16 © UCLES 2016 (b) Values of n and V are given in Fig. 2.2. Data: C = (2.7 ± 0.4) × 10–3 F n V / V X / 10–3 F / V–1 1 V 1 1.20 2 1.95 3 2.35 4 2.75 5 2.90 6 3.05 Fig. 2.2 Calculate and record values of X / 10–3 F and / V–1 1 V in Fig. 2.2. Include the absolute uncertainties in X. [3] (c) (i) Plot a graph of / V–1 1 V against X / 10–3 F. Include error bars for X. [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 9702/51/O/N/16 © UCLES 2016 [Turn over                     1 V /9² ;/ ²)

8 9702/51/O/N/16 © UCLES 2016 (iv) Determine the y-intercept of the line of best fit. Include the absolute uncertainty in your answer. y-intercept = …[2] (d) (i) Using your answers to (a), (c)(iii) and (c)(iv), determine the values of E and Y. Include an appropriate unit for Y. E = … V Y = … [2] (ii) Determine the percentage uncertainty in Y. percentage uncertainty in Y = … % [1] [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 5 printed pages. © UCLES 2016 [Turn over Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level PHYSICS 9702/51 Paper 5 Planning, Analysis and Evaluation October/November 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 October/November 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 – October/November 2016 9702 51 © UCLES 2016 Question Answer Marks 1 Defining the problem B is the independent variable and v is the dependent variable, or vary B measure v. 1 Keep starting position of magnet constant/magnet always released from rest. 1 Methods of data collection Labelled diagram showing a magnet and the vertical copper tube supported. 1 Method to ensure that copper tube is vertical, e.g. set square, spirit level, plumb line. 1 Method to determine time at bottom of tube e.g. use of light gate(s)/motion sensor attached to timer/datalogger/computer or distance between two fixed marks at bottom of tube and stopwatch. Do not allow time over length of tube. 1 Method to measure B, e.g. Hall probe. 1 Method of analysis Plot a graph of ln v against B. 1 λ = – gradient 1 v0 = ey-intercept 1

Page 3 Mark Scheme Syllabus Paper Cambridge International AS/A Level – October/November 2016 9702 51 © UCLES 2016 Question Answer Marks Additional detail including safety considerations 6 1. Keep mass of magnet constant. 2. Measurement of an appropriate length to determine v at bottom of tube, e.g. use ruler to measure distance between light gates/length of magnet/between two fixed marks. 3. v = d / t for appropriate lengths (not length of tube) 4. Adjust Hall probe until maximum reading obtained/perpendicular to field/pole or Use Hall probe to take readings for both poles and average. 5. Method to calibrate Hall probe using a known field. 6. Safety precaution linked to falling magnets/use sand tray/cushion to soften fall. 7. Repeat experiment with magnets reversed and average or Repeat v (or t) for same B and average. 8. ln v = –λB + ln v0 9. Relationship is valid if the graph is a straight line. 10. Method to vary B, e.g. re-magnetise in a coil.

Page 4 Mark Scheme Syllabus Paper Cambridge International AS/A Level – October/November 2016 9702 51 © UCLES 2016 Question Answer Marks 2 (a) gradient = 1 YE y-intercept = 1 E 1 (b) 2.7 or 2.70 0.833 or 0.8333 1.4 or 1.35 0.513 or 0.5128 0.90 or 0.900 0.426 or 0.4255 0.68 or 0.675 0.364 or 0.3636 0.54 or 0.540 0.345 or 0.3448 0.45 or 0.450 0.328 or 0.3279 All first column correct. Allow a mixture of significant figures. All second column correct. Allow a mixture of significant figures. Uncertainties in X from ± 0.4 to ± 0.07 (± 0.1). Allow more than one significant figure. 1 1 1 (c) (i) Six points plotted correctly. Must be within half a small square. No “blobs”. 1 All error bars in X plotted correctly. All error bars to be plotted. Length of bar must be accurate to less than half a small square and symmetrical. 1 (ii) Line of best fit drawn. Line must not be drawn from top point to bottom point. The lower end of line should pass between (0.95, 0.45) and (1.1, 0.45) and upper end of line should pass between (2.10, 0.70) and (2.25, 0.70). 1 Worst acceptable line drawn correctly. Steepest or shallowest possible line that passes through all the error bars. Mark scored only if all error bars are plotted. 1 (iii) Gradient determined with a triangle that is at least half the length of the drawn line. Read-offs must be accurate to half a small square. 1 Method of determining absolute uncertainty. uncertainty = gradient of line of best fit – gradient of worst acceptable line or uncertainty = ½(steepest worst line gradient – shallowest worst line gradient) 1 (iv) y-intercept determined correctly by substitution into y = mx + c. Read-offs must be accurate to half a small square. 1

Page 5 Mark Scheme Syllabus Paper Cambridge International AS/A Level – October/November 2016 9702 51 © UCLES 2016 Question Answer Marks Method of determining absolute uncertainty. uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line or uncertainty = ½(steepest worst line y-intercept – shallowest worst line y-intercept) No ECF from false origin method. 1 (d) (i) E = 1/y-intercept and given to 2 or 3 s.f. 1 gradient 1 × = E Y or gradient intercept − y Y in the range (0.90 to 1.20) × 10–3 F. Appropriate unit required. Correct substitution of numbers must be seen. 1 (ii) Percentage uncertainty in Y ∆ ∆   = + ×     100 m c m c or ∆ ∆   = + ×     100 m E m E or ∆ = × 100 Y Y Maximum/minimum methods: gradient min intercept max gradient min min 1 max − = × = y E Y gradient max intercept min gradient max max 1 min − = × = y E Y 1