Cambridge A Level Physics 9702 — 2012 Oct/Nov Paper 5 · Variant 3

1 Two identical light sources are viewed from a distance, as shown in Fig 1.1. When the angle For θ between the light sources is large, they are seen as separate. Examiner’s Use light source observer ș light source Fig 1.1 (not to scale) The sources are moved closer together. At a particular angle θ1 the two sources appear as a single source. It is suggested that θ1 is directly proportional to the wavelength λ of the light from the sources. Design a laboratory experiment using two light sources to test the relationship between θ1 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 (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) P λ is the independent variable or vary λ. [1] P θ is the dependent variable or measure θ (for each λ). [1] P Light sources to be of similar intensity/brightness. [1] Methods of data collection (5 marks) M1 Labelled diagram showing observer, light sources with method of producing monochromatic light e.g. filter/coloured LED. [1] M2 Method to measure wavelength: record from filter/LED or Young’s slit/diffraction grating method. [1] M3 Use a rule to measure the distances. [1] M4 Method to determine θ, e.g. θ (or sin θ or tan θ) = separation/distance or separation θ tan = ( 2 ) 2 × distance Do not allow protractor methods. [1] M5 Carry out the experiment in a dark room. [1] Method of analysis (2 marks) A Plot a graph of θ against λ. [Allow lg θ against lg λ]. [1] A Relationship valid if straight line through origin. [1] [If lg-lg then straight line with gradient = (+)1 (ignore reference to y-intercept)] Safety considerations (1 mark) S Lamp becomes hot, therefore do not touch/switch off when not in use or use gloves when moving hot lamp. OR Light may damage eyes, therefore wear dark glasses or do not look at unprotected lamps. [1] Additional detail (4 marks) D1/2/3/4 Relevant points might include [4] 1 Use vertical filament lamps. Allow vertical slits. 2 Additional detail on measuring λ e.g. use of equation for Young’s slit/diffraction grating method. 3 Use of vernier calipers to measure the separation of light sources. 4 Use large distances/separations. 5 θ = sin θ = tan θ for small angles. 6 View with the same eye. 7 Method to ensure distances are perpendicular or observer equidistant from pair of lamps. 8 Repeat experiment for each λ and average. Do not allow vague computer methods. [Total: 15] GCE AS/A LEVEL – October/November 2012 9702 53

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2 A trolley is attached to springs, as shown in Fig 2.1. When the trolley is displaced and then For released, the trolley oscillates. Examiner’s Use stand stand card light gate trolley springs springs Fig. 2.1 A student investigates how the maximum speed v of a trolley varies with the total mass M of the trolley. The maximum speed is determined using the time t taken for the card to pass through a light gate connected to an electronic timer. The length of the card is 5.0 ± 0.1 cm. Question 2 continues on the next page. It is suggested that v and M are related by the equation For Examiner’s k Use v = A M where A is the initial displacement and k is the spring constant of the springs. (a) A graph is plotted of v 2 on the y-axis against 1/M on the x-axis. Determine an expression for the gradient in terms of A and k. gradient = ................................................. [1] (b) Values of M and t are given in Fig. 2.2. M / kg t / s (1/M ) / kg–1 v 2 / m2 s–2 0.75 0.046 ± 0.002 1.25 0.058 ± 0.002 1.75 0.068 ± 0.002 2.25 0.078 ± 0.002 2.75 0.086 ± 0.002 3.25 0.092 ± 0.002 Fig. 2.2 Calculate and record values of (1/M ) / kg–1 and v 2 / m2 s–2 in Fig. 2.2. Include the absolute uncertainties in v 2. [3] (c) (i) Plot a graph of v 2 / m2 s–2 against (1/M ) / kg–1. Include error bars for v 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 uncertainty in your answer. gradient = ................................................ [2] 1.4 For Examiner’s Use 1.3 1.2 v 2 / m2 s–2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.2 0.4 0.6 0.8 1.0 1.2 1.4 (1 / M ) / kg–1

Mark scheme: 2 Analysis, conclusions and evaluation (15 marks) Part Mark Expected Answer Additional Guidance (a) A1 Gradient = kA2 (b) T1 T1 must be values in 1/M. Ignore row 2. T2 1.3 or 1.33 1.2 0.8(0)(0)(0) 0.74 T2 must be to 2 s.f. or 3 s.f. 0.571 or 0.54 or 0.55 0.5714 0.444 or 0.41 or 0.411 0.4444 or 0.410 0.364 or 0.34 0.3636 0.308 or 0.29 or 0.30 0.3077 U1 From ± 0.2 or ± 0.15 to ± 0.02 or Allow more than one significant figure. ± 0.03 Do not allow ± 0.1 for row 1. (c) (i) G1 Six points plotted correctly Must be within half a small square. Penalise ‘blobs’. Ecf allowed from table. U2 All error bars in v2 plotted Must be accurate within half a small square. correctly (c) (ii) G2 Line of best fit There must be a balance of points about the line of best fit – examiner judgement. Allow ecf from points plotted incorrectly. G3 Worst acceptable straight line. Line should be clearly labelled or dashed. Should Steepest or shallowest possible pass from top of top error bar to bottom of bottom line that passes through all the error bar or bottom of top error bar to top of bottom error bars. error bar. Mark scored only if error bars are plotted. (c) (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 0.9. U3 Uncertainty in gradient Method of determining absolute uncertainty. Difference in worst gradient and gradient. (d) (i) C2 k = gradient / A2 Should be about 22. = gradient / 0.04 C3 N m–1 Allow kg s–2 (d) (ii) U4 Percentage uncertainty in k ∆m ∆A ∆m × 100 + 2 × × 100 = × 100 + 5% m A m GCE AS/A LEVEL – October/November 2012 9702 53 (e) C4 v in the range 0.534 to 0.559 For 2 s.f. 0.53 to 0.56 and given to 2 or 3 s.f. U5 Uncertainty in v [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] ∆m ∆A ∆m Percentage uncertainty = × 100 + 2 × × 100 = × 100 + 5% m A m max m Maximum k = (min A ) 2 min m Minimum k = (max A ) 2 ∆k 1 (max k − min k ) Percentage uncertainty = × 100 = 2 × 100 k k (e) [U5] ∆A 1 ∆k Percentage uncertainty = × 100 + 2 × × 100 A k Absolute uncertainty = v × percentage uncertainty/100 max k Maximum v = max A× 0.75 min k Minimum v = min A × 0.75 Absolute uncertainty = max v – v or v – min v or 12 (max v − min v )

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