Cambridge A Level Physics 9702 — 2023 Feb/March Paper 5 · Variant 2

1 An electric pump is placed in a container of liquid. A model wind turbine is connected to the pump by a cable, as shown in Fig. 1.1. blades moving air pipe h cable pump wind turbine bench liquid Fig. 1.1 (not to scale) The turbine is placed in moving air. As the turbine blades turn, electricity is generated and the pump pushes liquid through a vertical pipe. The frequency of rotation of the turbine blades is f. The height the liquid moves is h. The mass per unit time of the liquid leaving the top of the pipe is Q. It is suggested that Q is related to f by the relationship Qgh = C + Df 3 where g is the acceleration of free fall, and C and D are constants. Plan a laboratory experiment to test the relationship between Q and f. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine values for C and D. 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 f is the independent variable and Q is the dependent variable, or vary f and measure Q. 1 Keep h constant 1 Methods of data collection Labelled diagram of workable experiment including: 1 • fan is positioned in line with the turbine so that blades of both fan and turbine overlap • base of fan on same bench as turbine • fan labelled and one other label from bench, (wind) turbine, cable, pump, pipe, liquid Labelled apparatus showing workable method to collect the liquid from the top of the pipe, e.g. hose / pipe / tube connected 1 to top of pipe with the other end over a beaker / measuring cylinder below top of pipe. At least one label related to collection of liquid. Use of stop-watch / timer to measure time to collect liquid or to measure time for blades to rotate. 1 Use of (top pan) balance to measure mass of liquid leaving the pipe. 1 Method of Analysis Plots a graph of Q against f 3 or equivalent (e.g. f 3 against Q). 1 Do not accept logarithmic graphs. C = gh -intercepty (for f 3 against Q: C = −D -intercepty ) 1 D = gh gradient 1 3 gh (for f against Q: D = ) gradient 1 Additional detail including safety considerations 6 Any six from: D1 Precaution with reason linked to prevent liquid spilling (on bench / floor) e.g. use of large bucket / bowl / tray to contain any spilled liquid or Precaution with reason linked to prevent air / dust particles in eye, e.g. use of goggles or Precaution with reason linked to turbine falling, e.g. clamp turbine to bench. D2 Use rule to measure h. D3 Method to determine mass of liquid, e.g. mass of beaker + liquid – mass of empty beaker or mass of container / pipe before – mass of container / pipe after. D4 Method to determine f, e.g. measure time t for many rotations / revolutions N and period T = t /N and f = 1/T or measure time t for many rotations / revolutions N and f = N/t or video rotating blades, playback frame by frame and use a time stamp to determine period T and f = 1/T. D5 Mark one of the blades to assist in counting number of rotations. D6 Method to vary f, e.g. change speed of fan / change distance between fan and blades / vary current in fan. D7 Wait for steady air flow before starting timing and / or collecting liquid. mass (of liquid) D8 Q = time (to collect liquid) or method and explanation to reduce uncertainty in Q, e.g. use large value of time or mass of liquid collected. D9 Repeat measurements of Q for the same value of f and average Q. 1 D10 Relationship valid if a straight line is produced (not passing through the origin). Do not accept passing through the origin.

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2 A student investigates standing waves in water. A sound source is placed at the bottom of a cylinder containing water. A microphone, attached to a rod, is placed above the sound source, as shown in Fig. 2.1. rod to oscilloscope to signal generator water microphone sound source bench Fig. 2.1 The sound source is connected to a signal generator. The microphone is connected to an oscilloscope. The signal generator is set to a frequency f. The microphone is moved up away from the sound source until the maximum amplitude is observed on the oscilloscope screen. The distance d1 between the microphone and sound source is measured. The microphone is moved up a further 2.0 cm. The microphone is then moved down until the maximum amplitude is observed on the oscilloscope screen. A second value d2 is measured. The average value of d is calculated. The experiment is repeated for different values of f. It is suggested that f and d are related by the equation v = 4 (d + k) f where v is the speed of sound in water and k is a constant. 1 (a) A graph is plotted of d on the y-axis against on the x-axis. f Determine expressions for the gradient and the y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of f, d1 and d2 are given in Table 2.1. Table 2.1 1 f / 103 Hz / 10–3 Hz–1 d1 / cm d2 / cm d / cm f 1.5 24.9 24.5 2.1 17.2 17.6 2.8 12.4 13.0 4.1 8.1 8.7 5.2 6.2 7.0 7.6 5.0 4.2 1 Calculate and record values of / 10–3 Hz–1 and d / cm in Table 2.1. f Include the absolute uncertainties in d. [2] 1(c) (i) Plot a graph of d / cm against / 10–3 Hz–1. f Include error bars for d. [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) v 1 gradient = 4 y-intercept = −k 2(b) 2 1/f / 10–3 Hz–1 d / cm 0.67 or 0.667 24.7  0.2 0.48 or 0.476 17.4  0.2 0.36 or 0.357 12.7  0.3 0.24 or 0.244 8.4  0.3 0.19 or 0.192 6.6  0.4 0.13 or 0.132 4.6  0.4 First mark: values of 1 / f and d correct as shown. Second mark: uncertainties in d correct as shown. 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 d / cm 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 Do not accept line from top plot to bottom plot. Points must be balanced. Line must pass between (0.170, 6.0) and (0.185, 6.0) and between (0.590, 22.0) and (0.610, 22.0) Worst acceptable line drawn. 1 Steepest or shallowest possible line that passes through all the error bars. All error bars must be plotted. 2(c)(iii) Gradient determined with clear substitution of data points into y / x; distance between data points must be greater than 1 half the length of the drawn line. Gradient determined of worst acceptable line uncertainty = (gradient of line of best fit – gradient of worst acceptable line) 1 or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 2(c)(iv) y-intercept determined by substitution of correct point with consistent power of ten in m and x into y = mx + c. 1 Expect y-intercept to be negative. y-intercept of worst acceptable line determined by substitution into y = mx + c. 1 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) 2(d) v determined using gradient and v and k given to 2 or 3 sf. 1 v = 4  gradient = 4  (c)(iii) k determined using y-intercept and units for v and k 1 k = − y -intercept = −(c)(iv) Units: v: m s–1, cm s–1 k: m, cm Absolute uncertainties in v and k. 1  gradient v:  v with correct substitution or v: 4  uncertainty in gradient gradient and k: uncertainty in y-intercept 2(e) f determined to a minimum of 2 significant figures from (c)(iii) and (c)(iv) OR (d) with correct substitution and correct 1 powers of ten used for all quantities. v f = 4  ( d + k ) or gradient f = d − ( y -intercept )

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