A student is investigating the motion of a small cube on a turntable connected to an electric motor as shown in Fig. 1.1. [Figure 1.1] The cube is placed at a distance r from the centre of the turntable. It is suggested that the relationship between r and the maximum frequency f of the turntable for which the cube does not move relative to the turntable is K = 4π²mfr where m is the mass of the cube and K is a constant. Design a laboratory experiment to test the relationship between f and r. 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 (May/June 2017). The mark or mark type is shown in brackets.

1. [1] r is the independent variable and f (frequency of turntable) is the dependent variable or vary r and measure f (frequency of turntable)
2. [1] keep m constant
3. [1] labelled diagram showing power supply connected to motor (two leads) within turntable; circuits must be workable
4. [1] method to change frequency of rotation of the turntable, e.g. adjust output of (variable) power supply or adjust variable resistor
5. [1] increase frequency until the cube moves (relative to the turntable)
6. [1] method to determine period of rotation of the turntable, e.g. stopwatch, light gate attached to a timer/data-logger or stroboscope
7. [1] plots a graph of f against 1 / r (allow log f against log r)
8. [1] relationship valid if a straight line produced passing through the origin (for lg f vs. lg r straight line of gradient of -1)
9. [1] K = gradient × 4π²m (for lg f vs. lg r, K = 10y-intercept × 4π²m)
10. [D1] use safety screen
11. [D2] time at least 10 rotations of turntable or detailed use of stroboscope
12. [D3] f = 1 / T for correct determination of period of rotation of turntable
13. [D4] repeat experiment for each r and average f
14. [D5] use balance to measure mass of cube
15. [D6] wait for turntable to rotate steadily before increasing frequency or gradual/incremental/slowly increase in frequency
16. [D7] use a spirit level to check that turntable is horizontal or clean cube/surface
17. [D8] use a rule to measure r
18. [D9] method to ensure r is measured to the centre of the cube, e.g. put a mark on the cube or align front or back of cube by a set distance
19. [D10] method to determine centre of the turntable e.g. measure two or more diameters/maximum distance ideas