A student is investigating the bending of a loaded wooden strip. Fig. 1.1 shows a rectangular strip of width b and thickness t overhanging the edge of a bench. A length L of the strip is unsupported. [Figure 1.1] A load of mass M is positioned at point P. This causes the unsupported part of the strip to bend with a deflection s, as shown in Fig. 1.2. [Figure 1.2 (not to scale)] It is suggested that the relationship between s and L is E = (4MgL³) / (bst³) where g is the acceleration of free fall and E is the Young modulus of the wood.

Mark scheme

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

1. L is the independent variable and s is the dependent variable or vary L and measure s
2. keep mass of load or M constant
3. labelled diagram of workable experiment including:
4. method of fixing strip at one end, e.g. with a G-clamp or (heavy) mass placed on top of strip over bench
5. load shown touching at point P
6. load and G-clamp or (heavy) mass labelled
7. method of attaching load to strip, e.g. use glue/tape/attach with a hook and string
8. use a rule to measure L and s
9. use a balance to measure M
10. plot a graph of s against L³ (allow Ig s against Ig L, or log)
11. relationship valid if a straight line through (0,0) (for Ig s against Ig L gradient of straight line = 3)
12. E = 4Mg / (bt³ x gradient)
13. (for Ig s against Ig L, E = 4Mg / bt³ ÷10⁻ᶦⁿᵗᵉʳᶜᵉᵖᵗ)
14. D1 use cushion/foam/sandbox in case mass/load falls or wear goggles in case strip snaps or recoils
15. D2 use same wooden strip or keep b and t constant
16. D3 clamp rule vertically to measure s
17. D4 method to ensure clamped rule to measure s is vertical, e.g. correctly positioned set square indicated at right angles to the horizontal surface or plumb line shown in appropriate position
18. D5 s = reading of vertical rule with loaded strip – reading of vertical rule with no load
19. D6 repeat s measurement for each L (unloading and loading strip) and average s
20. D7 use a micrometer/calipers to determine t
21. D8 repeat readings for b and/or t at different points along/across the strip and average
22. D9 method to ensure strip is perpendicular to the bench, e.g. repeat measurements of L on each side of strip to check that L is constant or set square correctly indicated on diagram
23. D10 wait until block is stationary/in equilibrium or measure s after a fixed time