Stretching a spring does work, and that work is stored as elastic potential energy, ready to be released. The store is the area under the force-extension graph, a triangle for a spring that obeys Hooke law.
The work done in stretching, and so the elastic potential energy stored, is the area under the force-extension graph. For a spring obeying Hooke law this is a triangle, Eₚ = ½Fx = ½kx². Elastic deformation is fully recovered when the load is removed; plastic deformation, beyond the elastic limit, is permanent.
Stretch the spring and watch the shaded triangle under the force-extension line grow. That area is the elastic potential energy, ½Fx, which also equals ½kx².
The behaviour changes at the elastic limit.
| Behaviour | Meaning | Energy |
|---|---|---|
| elastic | recovers fully when the load is removed | all stored energy returned |
| plastic | permanent change beyond the elastic limit | some energy not recovered |
Four quick checks tied to this lesson. Each correct answer earns XP and lights this skill on your star map.
The work done in stretching a spring is given on a force-extension graph by the:
The elastic potential energy stored in a spring obeying Hooke law is:
A spring of constant 200 N m⁻¹ is stretched by 0.10 m. The energy stored is:
Below the elastic limit, when the stretching force is removed, the spring:
The force-extension graph carries both the stiffness and the stored energy.
The stored energy is the triangle area ½Fx, not Fx; using the full rectangle doubles the answer. Because Eₚ = ½kx² depends on x², doubling the extension stores four times the energy. And beyond the elastic limit not all the work done is recovered, because energy goes into permanent (plastic) deformation and heating.
Unlocks once the checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
A force of 12 N stretches a spring obeying Hooke law by 0.060 m. The elastic potential energy stored is:
A metal wire is stretched beyond its elastic limit and the load is then removed. Compared with the work done in stretching it, the energy recovered is:
Two springs, of constants k and 2k, are stretched by the same extension x. The ratio of energy stored (first : second) is:
This skill is now lit gold on your star map. You have finished the lessons of Topic 6; the Paper 1 set awaits.