Cambridge A Level Physics 9702 — 2011 May/June Paper 5 · Variant 2

1 A student wishes to investigate projectile motion. For Examiner’s A small ball is rolled with velocity v along a horizontal surface. When the ball reaches the Use end of the horizontal surface, it falls and lands on a lower horizontal surface. The vertical displacement of the ball is p and the horizontal displacement of the ball is q, as shown in Fig 1.1. v p q Fig. 1.1 It is suggested that gq 2 = 2pv 2 where g is the acceleration of free fall. Design a laboratory experiment to investigate how q is related to p and how v may be determined from the results. 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 For problem data collection analysis considerations detail Examiner’s Use

Mark scheme: 1 Planning (15 marks) Defining the problem (3 marks) P1 p is the independent variable or vary p [1] P2 q is the dependent variable or measure q [1] P3 Keep (horizontal) velocity (v) constant [1] Methods of data collection (5 marks) M1 Labelled diagram of apparatus including method to vary p. [1] M2 Method to determine position of ball on surface e.g. carbon paper/dye/video/sand. [1] M3 Use ruler/caliper to measure p and/or q. [1] M4 Method to ensure velocity is constant e.g. releasing ball from same height on a track/ spring loaded device or impulse device set to a constant value. [1] M5 Method to ensure that the moved surface remains horizontal, e.g. spirit level/check height at different places. [1] Method of analysis (2 marks) A1 q2 against p q against p p against q2 p against q [1] g × gradient g g 1 g A2 v = v = gradient × v = v = × [1] 2 2 2× gradient gradient 2 Allow valid logarithmic graph e.g. lg q against lg p, lg 2p, lg 2p/g and valid calculation of v from y-intercept. Safety considerations (1 mark) S Reasoned method to prevent ball rolling on floor e.g. box below/storage box for balls/ sand box. Reasoned method to prevent ball causing injury e.g. goggles/safety screen [1] Additional detail (4 marks) D Relevant points might include [4] 1 Method to ensure that velocity of ball is horizontal only when it reaches table, e.g. curved track. 2 Ensure that the ball leaves the table at 90°, e.g. set square/protractor on upper surface. 3 Detail on measuring q – location of landing position e.g. centre of crater/start of track. 4 Detail on determining location of zero position for p and q e.g. set square, plumb line. 5 Detail on method of determining position of ball e.g. slow motion playback including scale. 6 Take many readings of q for each p and average. 7 Straight line through the origin shows that p is proportional to q2/relationship is valid – this mark may only be awarded when A1 is given. 8 Use of high density ball to minimise the effects of air resistance. Do not allow vague computer methods. [Total: 15] GCE AS/A LEVEL – May/June 2011 9702 52

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2 A student is investigating a non-inverting operational amplifier (op-amp) circuit. For Examiner’s The circuit is set up as shown in Fig. 2.1. Use +18 V + – E F –18 V V R Fig. 2.1 The op-amp is connected to a +18 V and –18 V power supply. E is the e.m.f. of the cell, which has a value of 1.6 ± 0.1 V. An experiment is carried out to investigate how the reading V on the voltmeter varies with resistance R. Question 2 continues on the next page. It is suggested that V and R are related by the equation For Examiner’s F Use V = E + E R where F is the resistance of the fixed resistor in the circuit. V 1(a) A graph is plotted of on the y-axis against on the x-axis. Express the gradient in E R terms of F. gradient = ..................................................[1] (b) Values of R and V are given in Fig. 2.2. R / Ω V / V 1 V / 10–3 Ω–1 R E 150 14.4 ± 0.1 220 10.4 ± 0.1 330 7.4 ± 0.1 470 5.6 ± 0.1 680 4.4 ± 0.1 860 3.8 ± 0.1 Fig. 2.2 1 V Calculate and record values of / 10–3 Ω–1 and in Fig. 2.2. Include the absolute R E V uncertainties in . [3] E V 1 V (c) (i) Plot a graph of against / 10–3 Ω–1. Include error bars for . [2] E R E (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] 11 For Examiner’s Use 10 V E 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 1 / 10–3 Ω–1 R

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Part Mark Expected Answer Additional Guidance (a) A1 F (b) T1 6.7 or 6.67 9.0 or 9.00 T1 for 1/R. T2 4.5 or 4.55 6.5 or 6.50 T2 for V/E. 3.0 or 3.03 4.6 or 4.63 Must be 2sf or 3sf; a mixture is allowed 2.1 or 2.13 3.5 or 3.50 1.5 or 1.47 2.8 or 2.75 1.2 or 1.16 2.4 or 2.38 U1 From ± 0.6 or ± 0.7, to ± 0.2 Allow more than one significant figure. (c) (i) G1 Six points plotted correctly Check second and fifth plots and other anomalous plots. Must be less than half a small square. Ecf allowed from table. U2 All error bars in V/E plotted correctly Half square or greater loses the mark. Ecf allowed from table. (ii) G2 Line of best fit If points are plotted correctly then lower end of line should pass between (0, 0.9) and (0, 1.1) and upper end of line should pass between (7, 9.3) and (7, 9.5). Allow ecf from points plotted incorrectly – examiner judgement. G3 Worst acceptable straight line. Line should be clearly labelled or dashed. Steepest or shallowest possible line Should pass from top of top error bar to that passes through all the error bars. 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. U3 Uncertainty in gradient Method of determining absolute uncertainty. Difference in worst gradient and gradient. (d) C2 (Gradient value) Ω Gradient must be used correctly. Expect about 1200 Ω Allow ecf from (c)(iii) but penalise POT. Do not penalise sf or rounding errors. U4 Determines uncertainty in F Allow ecf from POT. (e) (i) C3 Determines V/E correctly. Answer should be approximately 11; F from (d) must be used. F + 1 R U5 Determines absolute uncertainty Should be approximately 15% of RF/R1 (about 1.5). Several possible methods. (ii) C4 In the range 17.2 to 18.0 given to 2 or Allow 17 or 18 to 2sf. 3sf Must be (e)(i) × 1.6 [Total: 15] GCE AS/A LEVEL – May/June 2011 9702 52 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) [U4] Uncertainty = uncertainty in gradient (e) [U5] Uncertainty = worst V/E – V/E Note worst V/E is calculated either by max V/min E or by min V/max E Or max gradient of WAL/114 or min gradient of WAL/126  ∆m  F Uncertainty =  0.05 +  × [Allow V/E instead of F/R]  m  R  ∆F  F Uncertainty =  0.05 +  × [Allow V/E instead of F/R]  F  R  6 ∆m  F Uncertainty =  +  × [Allow V/E instead of F/R]  120 m  R  6 ∆F  F Uncertainty =  +  × [Allow V/E instead of F/R]  120 F  R

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