Cambridge A Level Physics 9702 — 2019 Oct/Nov Paper 5 · Variant 3

1 When a light plastic ball is placed in a vertical column of moving air, the ball becomes stationary at a height h, as shown in Fig. 1.1. ball h moving air air blower Fig. 1.1 A student is using an air blower to create the vertical column of moving air. The student connects the motor of the air blower to a d.c. power supply. It is suggested that the relationship between the radius r of the ball and h is 4 r r 3 gh = PK 3 where g is the acceleration of free fall, P is the power of the motor and K is a constant. Design a laboratory experiment to test the relationship between r and h. Explain how your results could be used to determine a value for K. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to: • 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 r is the independent variable and h is the dependent variable or vary r and measure/determine h 1 keep P constant 1 Methods of data collection labelled diagram of workable experiment including: • labelled air blower • labelled ball vertically (by eye) above the blower • vertical (by eye) rule at least from top of blower to ball 1 circuit diagram to determine P, e.g. voltmeter and ammeter connected to motor and power supply or wattmeter connected to motor and power supply 1 use of micrometer/calipers/rule to measure diameter of ball 1 measure the distance between the top/middle/bottom of the ball and the top of the blower 1 Method of Analysis plot a graph of h against 1 / r3 (or lg h against lg r) 1 relationship valid if a straight line through (0,0) (for lg h against lg r straight line with gradient = –3) 1 4 gradient 3 g K P π × = (for lg h against lg r, intercept 4 10 3 y g K P − π × = ) 1 Question Answer Marks 1 Additional detail including safety considerations D1 use large box/tray to collect ball (to prevent ball rolling on floor/bouncing) or reasoned method to avoid draughts, e.g. switch off fans, close windows, use a screen 6 D2 method to determine P from correct circuit, e.g. P = I × V or use wattmeter to measure P D3 stand on bench with clamped rule vertically to measure vertical distance D4 method to ensure clamped rule to measure h is vertical, e.g. correctly positioned set square indicated at right angles between the rule and the horizontal surface or plumb line shown in appropriate position D5 r = d / 2 when diameter measured D6 repeat diameter measurement in different directions and find average D7 repeat experiment for each value of r and determine average h D8 method to determine h, e.g. h = reading top of ball – r – top of blower or h = reading bottom of ball + r – top of blower or h = (distance from top of ball to top of blower + distance from bottom of ball to top of blower) / 2 D9 wait for the ball to become stationary (vertically) D10 video (camera) shown level with elevated ball and description of playback frame-by-frame or slow motion

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2 A student is investigating the oscillations of a mass attached to two springs connected in series, as shown in Fig. 2.1. springs mass Fig. 2.1 A stopwatch is used to measure the time t for 10 oscillations. The measurement of t is repeated and the average period T is determined. The experiment is repeated for different masses. It is suggested that T and mass M are related by the equation 2 r M q T = k where k is the spring constant of the two springs in series and q is a constant. (a) A graph is plotted of lg T on the y-axis against lg M on the x-axis. Determine expressions for the gradient and the y-intercept. gradient = ............................................................... y-intercept = ............................................................... [1] (b) Values of M, lg (M / g) and measurements of t are given in Fig. 2.2. M / g t / s t / s T / s lg (M / g) lg (T / s) 155 15.2 16.0 2.190 205 18.3 17.5 2.312 250 19.3 20.1 2.398 305 21.0 21.8 2.484 355 23.5 22.7 2.550 410 24.1 24.9 2.613 Fig. 2.2 Calculate and record values of T / s and lg (T / s) in Fig. 2.2. Include the absolute uncertainties in T / s and lg (T / s). [4] (c) (i) Plot a graph of lg (T / s) against lg (M / g). Include error bars for lg (T / s). [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 absolute uncertainty in your answer. gradient = ......................................................... [2]

Mark scheme: 2(a) gradient = q and y-intercept = π  = π −     2 1 lg lg 2 lg 2 k k 1 2(b) T / s lg (T / s) 1.56 0.193 or 0.1931 1.79 0.253 or 0.2529 1.97 0.294 or 0.2945 2.14 0.330 or 0.3304 2.31 0.364 or 0.3636 2.45 0.389 or 0.3892 Values of T as above. 1 Values of lg T as above. 1 Uncertainties in T all ±0.04. 1 Uncertainties in lg (T / s) consistent with uncertainties in T e.g. from ±0.011 to ±0.007. 1 Question Answer Marks 2(c)(i) Six points plotted correctly. Must be accurate to the nearest half a small square. Diameter of points must be less than half a small square. 1 Error bars in lg T plotted correctly. All error bars must be plotted. Length of bar must be accurate to less than half a small square and symmetrical. 1 2(c)(ii) Line of best fit drawn. Lower end of line should pass between (2.22, 0.22) and (2.25, 0.22) and upper end of line should pass between (2.49, 0.34) and (2.51, 0.34). Do not accept line from first to last plot. 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 from the line of best fit into ∆y / ∆x. Distance between data points must be greater than half the length of the drawn line. 1 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 from the line of best fit into y = mx + c. 1 2(d) k determined from y-intercept. 2 2 intercept 2 2 10 10 y k −   π π     = =               (c)(iv) 1 q = answer to (c)(iii) and given to 2 or 3 significant figures. 1 Question Answer Marks 2(e) M determined from (d) or (c)(iii) and (c)(iv) with correct substitution shown. 2 2 2 2 4 q q q T k k k M = = = π π π or π   −     = 2 (lg1) lg lg k M q = − = − -intercept lg gradient y M (c)(iv) (c)(iii) 10 M   −     = (c)(iv) (c)(iii) 1

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