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 4πr³gh = 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.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

1. [1] r is the independent variable and h is the dependent variable or vary r and measure/determine h
2. [1] keep P constant
3. [1] 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
4. [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
5. [1] use of micrometer/calipers/rule to measure diameter of ball
6. [1] measure the distance between the top/middle/bottom of the ball and the top of the blower
7. [1] plot a graph of h against 1/r³ (or lg h against lg r)
8. [1] relationship valid if a straight line through (0,0) (for lg h against lg r straight line with gradient = –3)
9. [1] K = (4πg × gradient) / (3P) (for lg h against lg r, K = (4πg × 10^(y-intercept)) / (3P))
10. 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
11. D2 method to determine P from correct circuit, e.g. P = I × V or use wattmeter to measure P
12. D3 stand on bench with clamped rule vertically to measure vertical distance
13. 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
14. D5 r = d/2 when diameter measured
15. D6 repeat diameter measurement in different directions and find average
16. D7 repeat experiment for each value of r and determine average h
17. 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
18. D9 wait for the ball to become stationary (vertically)
19. D10 video (camera) shown level with elevated ball and description of playback frame-by-frame or slow motion