Revision notes · Forces
Forces and elasticity
Forces and elasticity4.5.3
To stretch, compress, or bend an object, more than one force must be applied to it — a single force applied to a free object just makes it move (accelerate) rather than change shape. Deformation means a change of shape.
| Type of deformation | What happens when the load is removed | Example |
|---|---|---|
| Elastic deformation | The object returns to its original shape | An elastic band, stretched within its limits |
| Plastic deformation | The object does NOT return to its original shape — it stays permanently deformed | A spring stretched too far |
| Equation | Units |
|---|---|
| force = spring constant × extension — F = k × x | F in newtons (N), k in newtons per metre (N/m), x in metres (m) |
On a force–extension graph: while the line is straight (linear) through the origin, the spring is obeying Hooke's Law, and the gradient of the line equals the spring constant k. The point where the line stops being straight is the limit of proportionality — beyond this point the material no longer obeys Hooke's Law, and the extension increases non-linearly (a much bigger extension for the same extra force, if the material is soft, or none at all if it fractures instead).
| Equation | Units |
|---|---|
| elastic potential energy stored = ½ × spring constant × extension² — Eₑ = ½ × k × x² | Eₑ in joules (J), k in N/m, x in m |
When a force stretches or compresses a spring, work is done on the spring, storing energy in its elastic potential energy store. Provided the spring deforms elastically (not plastically), the work done on the spring equals the elastic potential energy stored in it.
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