Forces and Elasticity (Hooke's Law) — AQA GCSE Physics
Stretching, compressing or bending an object changes its shape, and for elastic objects the extension is proportional to the force.
Elastic and inelastic deformation
To change the shape of an object, more than one force must act on it (otherwise it would just move). Deformation is:
- Elastic — the object returns to its original shape when the forces are removed (e.g. a spring within its limit).
- Inelastic — the object stays deformed.
Hooke's law
For an elastic object such as a spring, the extension is directly proportional to the force applied, up to the limit of proportionality:
$$F = k \times e$$
- F = force (N), k = spring constant (N/m), e = extension (m).
The spring constant (k) measures the stiffness — a stiffer spring has a larger k.
Force–extension graphs
A force–extension graph is a straight line through the origin (obeying Hooke's law) until the limit of proportionality, after which it curves.
Required practical and elastic potential energy
In the required practical, you hang masses on a spring and measure the extension. The work done in stretching an elastic object (within the limit) is stored as elastic potential energy: $E_e = \tfrac12 k e^2$.
Exam tips
- Extension is directly proportional to force up to the limit of proportionality.
- Learn F = ke; the spring constant k is the stiffness.
- A force–extension graph is linear then curves beyond the limit.
- Work done stretching is stored as elastic potential energy.