A student is investigating the stability of a wooden block resting on a bench. A strip is attached by a nail to the centre of the top of the block and is able to rotate, as shown in Fig. 1.1 and Fig. 1.2. [Figure 1.1] [Figure 1.2] A load of mass m is attached to the free end of the strip at point P. The student is investigating the position of the strip indicated by angle θ, as shown in Fig. 1.2, at which the block just topples. It is suggested that the relationship between m and θ is αVw = 2mL cos θ – mw where α is a constant, V is the volume of the block, w is the width of the block and L is the distance between the centre of the nail and the centre of the load. Design a laboratory experiment to test the relationship between m and θ. Explain how your results could be used to determine a value for α. 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 2019). The mark or mark type is shown in brackets.

1. [1] m is the independent variable and θ is the dependent variable or vary m and measure θ
2. [1] or θ is the independent variable and m is the dependent variable or vary θ and measure m
3. [1] keep position of load constant or L constant
4. [1] labelled diagram of workable experiment including: • load shown touching at P • load labelled and at least one other label
5. [1] use a protractor to measure θ
6. [1] if m is the independent variable: (slowly) change the angle until the block (just) topples
7. [1] or if θ is the independent variable: (slowly) change mass until block (just) topples
8. [1] use a balance to measure m
9. [1] plot a graph of cos θ against 1 / m (or reverse axes 1 / m against cos θ) (not 1 / cos θ against m or m against 1 / cos θ)
10. [1] relationship valid if a straight line (not 'through the origin' unless the choice of axes indicates the intercept is zero)
11. [1] α = (2L x gradient) / (V x w) or α = gradient / (V × y-intercept)
12. [1] for reverse axes: α = 2L / (V x w x gradient) or α = 1 / (V × y-intercept)
13. D1 use cushion/foam/sandbox in case block/load falls
14. D2 measure L with a rule
15. D3 correctly positioned protractor to measure θ, e.g. protractor with its centre over the nail and its straight edge parallel to an edge of the block
16. D4 method to fix m to strip
17. D5 method to determine volume of block, e.g. V = w × h × l
18. D6 measure w, h and l with calipers/micrometer/rule
19. D7 (if m is the independent variable:) repeat experiment for θ and determine the average θ or (if θ is the independent variable:) repeat experiment for m and determine the average m
20. D8 equation must be in the form of y = mx + c with cos θ on one side and m on the other side e.g. for a graph of cos θ against 1/m: cos θ = (αVw / 2Lm) + (w / 2L) or for a graph of 1 / m against cos θ: 1 / m = (αVw / 2Lcos θ) + (1 / αV)
21. D9 method to determine centre of load or centre of block e.g. measure diameter/width and halve or diagonals across the block
22. D10 method to ensure that block or strip is horizontal, e.g. check with a spirit level that table/block is horizontal or use a rigid strip