Cambridge A Level Physics 9702 — 2022 Oct/Nov Paper 5 · Variant 2

1 A thin copper sheet is suspended from a small hole near the top of the sheet and placed in a magnetic field, as shown in Fig. 1.1. z hole copper sheet area A direction of magnetic field Fig. 1.1 (not to scale) The sheet has area A and thickness z. The sheet is displaced from its equilibrium position and then released so that it oscillates perpendicular to the direction of the magnetic field. The time t from when the sheet is released to when it becomes stationary is measured. It is suggested that t is related to z by the relationship Kz q t = ABρ where B is the magnetic flux density of the field, ρ is the density of copper, and K and q are constants. Plan a laboratory experiment to test the relationship between t and z. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine values for K 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: Question Answer Marks 1 Defining the problem z is the independent variable and t is the dependent variable or vary z and measure t 1 keep B and A constant 1 Methods of data collection labelled diagram of workable experiment including: 1 • pin/rod though hole • supported by a stand • sheet able to oscillate freely • at least one label from copper/sheet, hole, clamp stand, rod, pin use of stop-watch/timer to measure t (from release to stopping) 1 or use of stop-watch/timer to measure time for the sheet (to stop) oscillating use of micrometer to measure z 1 use of rule(r) to measure lengths to determine A 1 and A = length  breadth Method of Analysis plot a graph of lg t against lg z or equivalent (e.g. ln t against ln z) 1 q = gradient 1 K = AB 10y -intercept 1 ( K = AB ey -intercept for ln t against ln z) 1 Additional detail including safety considerations 6 D1 use of cushion / sand box in case sheet falls or use gloves to protect hands from cuts / sharp edges D2 keep (initial) distance between (copper) sheet and (poles of) magnet constant or keep (initial) distance between (copper) sheet and coil(s) constant D3 keep initial displacement (of copper sheet) constant D4 method to ensure initial displacement (of copper sheet) is constant, e.g. initially line up (corner of) plate with fiducial marker/vertical pin  K  D5 relationship valid if a straight line (with y-intercept = log   ) is produced  AB D6 repeat measurements of z in different positions and average z D7 measure B / magnetic flux density using a (calibrated) Hall probe D8 additional detail on use of Hall probe, e.g. adjust (position of) probe until maximum value or measure B using Hall probe first in one direction and then in the opposite direction and average D9 drawn method to create a magnetic field perpendicular to the area of the sheet, e.g. pair of magnets/horseshoe magnet/pair of coils connected to a (d.c.) supply D10 repeat experiment for each z and average t D11 method to determine , e.g. measure mass with balance and volume = Az and density = mass / volume

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2 A student investigates stationary waves in a vertical tube using the apparatus shown in Fig. 2.1. from signal generator to oscilloscope loudspeaker stand tube bench Fig. 2.1 The student slowly increases the frequency of the signal generator from zero and listens to the sound. The loudness of the sound varies several times between minimum and maximum as the frequency is increased. The lowest frequency giving maximum loudness is identified by n = 1. The next frequencies giving maximum loudness are identified by n = 2, 3, 4, 5 and 6. For each value of n, the student observes the trace on the oscilloscope screen. The student measures the distance d on the screen between two successive crests, as shown in Fig. 2.2. d Fig. 2.2 The student then determines the period T and frequency f of the signal. It is suggested that f and n are related by the equation (2n – 1)c f = 4h where c is the speed of sound in air and h is the height of the tube. (a) A graph is plotted of f on the y‑axis against n on the x‑axis. Determine expressions for the gradient and y‑intercept. gradient = ............................................................... y‑intercept = ............................................................... [1] (b) The period T and frequency f are given by the equations 1 T = d × time‑base and f = . T Values of n, d and the time‑base of the oscilloscope are given in Table 2.1. Table 2.1 time‑base n d / cm T / ms f / Hz / ms cm–1 1 1.4 ± 0.2 5 2 2.9 ± 0.2 1 3 3.6 ± 0.2 0.5 4 2.7 ± 0.2 0.5 5 2.1 ± 0.2 0.5 6 8.8 ± 0.2 0.1 Calculate and record values of T / ms and f / Hz in Table 2.1. Include the absolute uncertainties in T and f. [2] (c) (i) Plot a graph of f / Hz against n. Include error bars for f. [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) c 1 gradient = 2h c y-intercept = − 4h 2(b) 1 T / ms f / Hz 7.0 or 7.00 ± 1 140 or 143 ± (10–30) 2.9 or 2.90 ± 0.2 340 or 345 ± (20–30) 1.8 or 1.80 ± 0.1 560 or 556 ± 30 1.4 or 1.35 ± 0.1 710 or 714 ± (40–60) or 740 or 741 1.1 or 1.05 ± 0.1 910 or 909 ± (80–100) or 950 or 952 0.88 or 0.880 ± 0.02 1100 or 1140 ± (30–60) Values of T and f correct as shown above. Absolute uncertainties in T and f correct as shown above. 1 2(c)(i) Six points from (b) plotted correctly. 1 Must be within half a small square. Diameter of points must be less than half a small square. Error bars in f plotted correctly. 1 All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical. 2(c)(ii) Straight line of best fit drawn. 1 Points must be balanced. Do not accept line from top point to bottom point. Line must pass between (2.20, 400) and (2.40, 400) and (5.20, 1000) and (5.60, 1000). Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). 1 All error bars must be plotted. 2(c)(iii) Gradient determined with clear substitution of data points into y / x. 1 Distance between data points must be greater than half the length of the drawn line. Gradient of worst acceptable line determined with clear substitution of data points into y / x. 1 uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 2(d) 83.2 ± 0.3 (cm) 1 2(e)(i) c determined using gradient and c given to two or three significant figures. 1 c = 2  h  gradient = 2  (d)  (c)(iii) c determined using gradient and given with correct SI unit and correct power of ten: m s–1 or cm s–1. 1 2(e)(ii) Percentage uncertainty in c from (c)(iii) and (d) with method shown. 1  h gradient  percentage uncertainty =  +   100  h gradient  or correct substitution for max/min methods: max c = 2  max h  max gradient min c = 2  min h  min gradient 2(f) h determined to at least two significant figures from (e)(i) with correct substitution. 1 3  (e)(i) h = 4  130 Absolute uncertainty in h determined. Correct substitution must be seen. 1  f c   5 c  h = +  h = +  h      f c   130 c  or correct substitution for max/min methods: 3  max c 3  max (e)(i) max h = = 4  min f 4  125 3  min c 3  min(e)(i) min h = = 4  max f 4  135

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