Cambridge A Level Physics 9702 — 2022 Feb/March Paper 5 · Variant 2

1 A trolley with a magnet attached is placed on a thin steel sheet as shown in Fig. 1.1. trolley magnet S d N steel sheet X bench θ Fig. 1.1 The angle between the sheet and the bench is θ. The distance from point X to the trolley is d. The trolley is released from rest and travels down the slope. The velocity v of the trolley at X is determined using a light gate. It is suggested that v is related to θ by the relationship mv 2 mp sin θ – qB = 2d where m is the mass of the trolley and magnet, B is the magnetic flux density between the magnet and the steel sheet, and p and q are constants. Plan a laboratory experiment to test the relationship between v and θ. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine values for p and q. In your plan you should include: • 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. 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Mark scheme: 1 Defining the problem θ is the independent variable and v is the dependent variable, or vary θ and measure v. 1 Keep d constant 1 Methods of data collection Labelled diagram of workable experiment including: • sheet supported by stand / jack • light gate positioned at X • support, light gate and X labelled. 1 Light gate connected to timer / datalogger. 1 Measure length (L) (of card) interrupted by beam for single light gate. 1 Method to measure θ, e.g. use protractor or Method to determine θ , e.g. use a rule(r) to measure two appropriate distances to use in a trigonometrical ratio 1 Method of Analysis Plots a graph of v2 on y-axis and sin θ on x-axis. Allow other valid graphs, e.g. sin θ against v2 Do not accept log graphs. 1 gradient 2 p d = for v2 against sin θ or 1 2 gradient p d = × for sin θ against v2 1 Question Answer Marks 1 intercept 2 m y q Bd × − = − for v2 against sin θ or intercept intercept 2 gradient mp y m y q B dB × − × − = = × for sin θ against v2 1 Additional detail including safety considerations Any six from: 6 D1 Method to stop the trolley once the trolley passes X, e.g. place a block / stop on the bench near the end of the sheet Ignore trolley falls D2 Keep B and m constant D3 Use a rule(r) to measure d D4 Method to keep d constant, e.g. mark distance d on the sheet or the starting position of the trolley on the sheet D5 Method to measure mass of trolley (and magnet), e.g. use balance or use newton meter to measure weight and divide by g and Measure B using a (calibrated) Hall probe D6 Additional detail on use of Hall probe, e.g. adjust probe until maximum value or measure B using Hall probe first in one direction, then in the opposite direction and average D7 Determine v (the velocity at X) from L / t (for a single light gate) D8 Additional detail on measuring θ, e.g. protractor drawn in correct position on diagram, or additional detail on determining θ , e.g. relationship between measured lengths and θ Question Answer Marks 1 D9 Relationship valid if a straight line is produced (not passing through the origin) D10 Repeat experiment for each θ and average v.

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2 A student investigates a circuit containing a capacitor and a resistor as shown in Fig. 2.1. C a.c. power to dual-beam supply oscilloscope R Fig. 2.1 A dual‑beam oscilloscope is connected across the capacitor of capacitance C and resistor of resistance R. The oscilloscope displays two traces as shown in Fig. 2.2. Fig. 2.2 The student determines the phase difference θ between the two traces. The student repeats the experiment with different resistors. It is suggested that θ and R are related by the equation 1 tan θ = 2πfCR where f is the frequency of the a.c. power supply. 1 (a) A graph is plotted of tan θ on the y‑axis against on the x‑axis. R Determine an expression for the gradient. gradient = ......................................................... [1] (b) Values of R and θ are given in Table 2.1. Each value of R has a percentage uncertainty of ± 5%. Table 2.1 1 R / Ω / 10–3 Ω–1 θ/ ° tan θ R 12 80.8 16 77.5 22 73.0 33 65.2 39 61.7 43 59.3 1 Calculate and record values of / 10–3 Ω–1 and tan θ in Table 2.1. R 1 Include the absolute uncertainties in R. [2] 1(c) (i) Plot a graph of tan θ against / 10–3 Ω–1. R 1 Include error bars for R. [2] (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Label both lines. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = ......................................................... [2]

Mark scheme: 2(a) Gradient = 1 2 fC π 1 2(b) 1 R / 10–3 Ω–1 tan θ 83 or 83.3 6.17 or 6.174 63 or 62.5 4.51 or 4.511 45 or 45.5 3.27 or 3.271 30 or 30.3 2.16 or 2.164 26 or 25.6 1.86 or 1.857 23 or 23.3 1.68 or 1.684 1 Absolute uncertainties in 1 R from ± 4 to ± 1 1 Question Answer Marks 2(c)(i) Six points from (b) plotted correctly. Must be within half a small square. Diameter of points must be less than half a small square. 1 Error bars in 1 R plotted correctly. All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 1 2(c)(ii) Straight line of best fit drawn. Points must be balanced. Do not accept line from top plot to bottom plot. Line must pass between (33.5, 2.5) and (35.0, 2.5) and (74.0, 5.5) and (76.0, 5.5) 1 Worst acceptable line drawn. Steepest or shallowest possible line that passes through all the error bars. All error bars must be plotted. 1 2(c)(iii) Gradient determined with clear substitution of data points into Δy/Δx; distance between data points must be greater than half the length of the drawn line. 1 Gradient determined of WAL with clear substitution of data points into Δy/Δx; uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 1 2(d) 99 ± 2 (Hz) 1 2(e)(i) C determined using gradient and C given to two or three significant figures. 1 1 2 gradient 2 C f = = π × π× × (d) (c)(iii) 1 C determined using gradient with correct SI unit and power of ten for C: F or s Ω–1 1 Question Answer Marks 2(e)(ii) Percentage uncertainty in C determined with method shown. gradient %uncertainty 100 gradient f f   Δ Δ = + ×     OR Correct substitution for max/min methods 1 max 2 min mingradient C f = π × × 1 min 2 max maxgradient C f = π× × 1 2(f) R determined to at least two significant figures with appropriate power of ten from (c)(iii) OR (d) and (e)(i) with correct substitution seen. gradient tan 0.839 R θ = = (c)(iii) OR 1 1 2 tan 2 0.839 R fC θ = = π π× × × (d) (e)(i) 1 Absolute uncertainty in R determined. Method must be consistent with determination of R and correct substitution must be seen. For R determined by using the gradient: gradient gradient R R Δ Δ = × OR For R determined by using (d) and (e)(i): f C R R f C Δ Δ   Δ = + ×     OR ΔR determined by max / min methods. 1

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