A student is investigating how the extension e of an elastic cord depends on the diameter d of the cord when a force is applied. The student has a number of elastic cords of the same material with different diameters. The elastic cords have circular cross-sections. Each cord has an unstretched length of approximately 50 cm. It is suggested that the extension e and the cross-sectional area A of the cord are related by the expression E = FL / Ae where E is the Young modulus of the material of the cord, F is the force applied and L is the unstretched length of the cord. Design a laboratory experiment to test the relationship between e and d. Explain how your results could be used to determine a value for E. 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 (Feb/Mar 2018). The mark or mark type is shown in brackets.

1. [1] d is the independent variable and e is the dependent variable, or vary d and measure e.
2. [1] Keep F constant.
3. [1] Labelled workable diagram including elastic cord fixed at one end to a support and load attached to the other end
4. [1] Cord and weight must be labelled
5. [1] Use of ruler to measure unstretched length and stretched length.
6. [1] or labelled ruler drawn parallel to cord and original length L and either e or stretched length indicated.
7. [1] Use of a micrometer / (calipers) to determine d.
8. [1] Weigh load on a balance or use of balance to measure mass of load and multiply by g
9. [1] Plots a graph of e against 1 / d² or equivalent
10. [1] Relationship valid if a straight line passing through the origin is produced
11. [1] E = 4FL / (gradient × π)
12. [1] Use safety goggles / safety screen to prevent injury to eyes from (moving) elastic cord/load or use cushion / sand box in case load falls.
13. [1] Keep L constant
14. [1] Method to keep L constant, e.g. check length of each cord / adjust through cork
15. [1] Additional detail on measuring e, e.g. record initial position, record final position and subtract
16. [1] Repeat measurement of d along cord / different diameters and average
17. [1] Method to ensure Hooke’s law is obeyed, e.g. check that the length is constant after removing load or do not exceed elastic limit
18. [1] Wait for cord to extend to its maximum value / stop oscillating
19. [1] Use of A = πd² / 4
20. [1] Use of set square to check that ruler is vertical to bench, or use of set square as a fiducial mark to read measurements