Cambridge A Level Physics 9702 — 2024 May/June Paper 5 · Variant 1

1 Fig. 1.1 shows a small solid metal cylinder of mass m, length L and diameter d. L d Fig. 1.1 The cylinder is heated to a uniform temperature. The cylinder is then removed from the heat source and the cylinder is wrapped in an insulating material. The temperature of the room is TR. At time t after the cylinder starts to cool, the surface temperature of the cylinder is TC. It is suggested that TC is related to t by the relationship UAt – (TC – TR) = Ze mc where A is the total surface area of the cylinder, c is the specific heat capacity of the metal, and U and Z are constants. Plan a laboratory experiment to test the relationship between TC and t. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine values for U and Z. 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 t is the independent variable and TC is the dependent variable or vary t and measure TC 1 keep TR constant 1 Methods of data collection labelled diagram of workable experiment including:  solid cylinder cooling  insulation surrounding all of the cylinder  thermometer touching cylinder inside insulation  insulation and thermometer labelled 1 method to heat the cylinder uniformly, e.g. place in oven/immerse in hot water or diagram showing cylinder in oven or hot water 1 method to determine time t, e.g. stopwatch or temperature sensor connected to a data logger 1 method to measure L e.g. use a ruler/calipers/micrometer and method to measure d e.g. use calipers/micrometer 1 Method of Analysis plot a graph of ln (TC – TR) against t or equivalent 1 gradient mc U A   1 Z = ey-intercept 1 Question Answer Marks 1 Additional detail including safety considerations 6 D1 precaution to prevent burns or use of hot cylinder / oven / hot water e.g. use of gloves, use of tongs D2 keep thickness of the insulating material constant (for each TC) D3 method to measure m, e.g. use a (top-pan) balance D4 for water bath/oven methods, wait for initial temperature of the cylinder to become uniform or constant throughout the cylinder D5 (surface)    2 2 d A dL or          2 2 4 d dL D6 repeat measurements of d along the length of the cylinder / in different directions and determine the average value of d D7 description of how c is determined from a separate experiment by heating the cylinder using electrical heater and E c m     D8 method of determining energy supplied to electrical heater to determine c, e.g. use of joulemeter for E or electrical method using ammeter and voltmeter to determine IVt D9 use several temperature sensors and determine the average TC D10 relationship valid if a straight line is produced (with y-intercept = ln Z) Do not accept line passing through the origin.

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2 A student investigates the sound from a horn attached to a car, as shown in Fig. 2.1. v horn Frequency: 894.2 Hz Fig. 2.1 (not to scale) A microphone is placed at the side of the road and connected to a frequency meter. The car travels towards the microphone. The frequency f of the sound detected by the microphone is read from the frequency meter. The speed of the car is measured by two speed detectors. The two measurements of speed are v1 and v2. The average speed v of the car is determined from v1 and v2. The experiment is repeated for different speeds of the car. It is suggested that f and v are related by the equation fsk f = k – v where fs is the frequency of the sound emitted by the horn and k is a constant. 1 (a) A graph is plotted of on the y-axis against v on the x-axis. f Determine expressions for the gradient and y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of v1, v2 and f are given in Table 2.1. Table 2.1 1v1 / m s–1 v2 / m s–1 v / m s–1 f / Hz / 10–3 Hz–1 f 3.1 3.9 894.2 6.7 5.9 901.2 9.2 8.2 908.0 11.9 10.9 915.8 13.3 14.5 923.6 15.6 16.8 931.2 1 Calculate and record values of v / m s–1 and / 10–3 Hz–1 in Table 2.1. f Include the absolute uncertainties in v. [2] 1(c) (i) Plot a graph of / 10–3 Hz–1 against v / m s–1. Include error bars for v. [2] f (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 s kf  y-intercept = 1 sf 1 2(b) v / m s–1 1 f / 10–3 Hz–1 3.5  0.4 1.118 or 1.1183 6.3  0.4 1.110 or 1.1096 8.7  0.5 1.101 or 1.1013 11.4  0.5 1.092 or 1.0919 13.9  0.6 1.083 or 1.0827 16.2  0.6 1.074 or 1.0739 Values of v and 1 f correct as shown above. 1 Uncertainties in v correct as shown above. 1 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 v 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 Question Answer Marks 2(c)(ii) Straight line of best fit drawn. Do not accept line from top point to bottom point. Line must pass between (14.5, 1.080) and (14.9, 1.080) and between (4.5, 1.115) and (4.8, 1.115). 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 y / x. Gradient must be negative. Distance between data points must be greater than half the length of the drawn line. 1 Gradient determined of worst acceptable line with clear substitution of data points into y / x. 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(c)(iv) y-intercept determined by substitution of correct point with consistent power of ten in m and y into y = mx + c. 1 y-intercept of worst acceptable line determined by substitution into y = mx + c. 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) Do not accept ECF from false origin method. 1 Question Answer Marks 2(d)(i) fs determined using y-intercept and fs given to 2, 3 or 4 significant figures and k given to 2 or 3 significant figures. 1 -intercept sf y  1 k determined using gradient with method shown and fs and k given with SI units with appropriate powers of ten. -intercept gradient y k  or 1 gradient s k f   Units of fs: Hz Units of k: m s–1 1 2(d)(ii) Percentage uncertainty in k with method shown.            -intercept gradient percentage uncertainty 100 -intercept gradient y y or correct substitution for max/min methods. 1 2(e) v determined (non-zero) to a minimum of 2 significant figures from (c)(iii) and (c)(iv) or (d)(i) with correct substitution. 1 -intercept gradient y f v   or s kf v k f   1

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