Forces and elasticity

Elastic vs inelastic deformation

When a force stretches, compresses or bends an object it deforms.

• Elastic deformation — the object returns to its original shape when the force is removed (e.g. a spring under a small load).
• Inelastic deformation — the object stays permanently deformed (e.g. a stretched paper clip).

To deform an object, more than one force must act — pulling at one end alone simply moves it. A spring being stretched has the load pulling down and the support pushing up.

Hooke’s law

For a spring stretched within its limit of proportionality, the extension is directly proportional to the force applied.

F = k × e

• F = force applied (N)
• k = spring constant (N/m) — a measure of stiffness
• e = extension from the natural length (m)

A stiffer spring has a larger k and stretches less for the same force.

A force–extension graph for a spring is a straight line through the origin up to the limit of proportionality, then curves above it (Hooke’s law no longer holds).

Elastic potential energy stored

When a spring is stretched or compressed elastically, work is done on it and energy is stored as elastic potential energy:

E = ½ × k × e²

Units: J. Note the squared — doubling the extension stores four times the energy.

Determining the spring constant (Core Practical link)

1. Hang a spring from a clamp and measure its natural length with a ruler.
2. Add masses (e.g. 100 g = 0.98 N) one at a time; measure the new length each time.
3. Calculate extension = new length − natural length for each load.
4. Plot force (y-axis) against extension (x-axis).
5. The gradient of the straight portion = the spring constant k.

Edexcel exam tip

Always convert cm to m before calculating with k or E. The most common dropped mark on this topic is "extension in cm". Also, never quote E = ½ × F × e for elastic PE — Edexcel’s mark scheme requires k and e².