Not given in the exam, recall it.
What it is for
Hooke's law is used in Force and Motion II (SPM Physics Form 5). Keep the SI units in every line of working. Force and Motion II
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| F | force | N |
| k | spring (force) constant | N m⁻¹ |
| x | extension | m |
Rearrangements
k = F / xx = F / k
Worked example
Common trap
Understanding Hooke's law
Hooke's law F = kx describes how a spring stretches. F is the applied force in newtons (N). k is the spring (force) constant in newtons per metre (N m⁻¹), a measure of stiffness. x is the extension, the increase in length, in metres (m).
Force and extension are directly proportional: double the force and the extension doubles, provided you stay within the elastic limit. A stiffer spring has a larger k, so it stretches less for the same force.
Rearrange as needed: k = F / x finds the spring constant from a force–extension measurement, and x = F / k predicts how far a known spring will stretch. Always use the extension x, not the spring's total length.
A worked example, step by step
A force of F = 15 N stretches a spring by an extension of x = 0.06 m. Find the spring constant.
Rearrange Hooke's law for k:
- k = F / x = 15 N / 0.06 m
- k = 250 N m⁻¹
So the spring constant is k = 250 N m⁻¹ (3 significant figures). This means each additional metre of stretch would need 250 N, or each extra centimetre needs 2.5 N.
Check by predicting: a 30 N force should give x = F/k = 30 / 250 = 0.12 m, exactly double the original extension, which is what direct proportionality demands.
Common mistakes and how this is tested
The key trap: x is the extension (change in length), not the total length, and the law is valid only up to the elastic limit.
Other common errors:
- Leaving x in centimetres, so k comes out 100 times too small.
- Using the spring's loaded length instead of subtracting its natural length.
- Applying the law beyond the elastic limit, where the graph is no longer straight.
Questions ask you to calculate k, F or x, to define the spring constant, or to explain the shape of a force–extension graph and where the elastic limit lies.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)