HOOKE'S LAW
5 marks · HardA student is testing the behaviour of a metal wire using the setup below. She measures its original length as 80.0 cm. She applies a series of increasing forces and records the following lengths:
| Force / N | Length / cm |
|---|---|
| 0 | 80.0 |
| 2 | 80.4 |
| 4 | 80.8 |
| 6 | 81.2 |
| 8 | 81.6 |
| 10 | 82.8 |
Calculate the extension produced by each applied force, entering your answers in cm.
Identify between which two forces the wire most likely stops obeying Hooke’s law, and justify your answer using the data.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 0.0, 0.4, 0.8, 1.2, 1.6, 2.8 (cm extensions) cm · must show Extension column: length minus original length
(b) Between 8 N and 10 N; because the increase in extension between these forces (1.2 cm) is much greater than previous increases (all 0.4 cm per 2 N), so it is no longer proportional to the applied force. · must show States correct interval (8 N – 10 N), Recognises disproportional jump, References data as justification
Common mistakes: Calculating from wrong starting length; Confusing extension with length
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Subtracts original length from each reading to get extension
A1 (a) · 1 mark · All extensions calculated as: 0.0, 0.4, 0.8, 1.2, 1.6, 2.8 cm
M2 (b) · 1 mark · Identifies the interval between 8 N and 10 N as point of non-linearity
B1 (b) · 1 mark · References that the jump in extension is much larger than for previous forces
B2 (b) · 1 mark · States that this means the wire stops obeying Hooke’s law (is no longer proportional)
Worked solution
| Force / N | Length / cm | Extension / cm |
|---|---|---|
| 0 | 80.0 | 0.0 |
| 2 | 80.4 | 0.4 |
| 4 | 80.8 | 0.8 |
| 6 | 81.2 | 1.2 |
| 8 | 81.6 | 1.6 |
| 10 | 82.8 | 2.8 |
From 0–8 N, the extension increases by 0.4 cm for each additional 2 N. From 8 N to 10 N, the extension increases by 1.2 cm, much greater than before. This shows the wire stops obeying Hooke’s law between 8 N and 10 N, as extension is no longer proportional to force.