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Hooke's law limits
Intermediate
Beyond the elastic limit, deformation is permanent.
Hooke's law holds only up to the proportional limit. Beyond the elastic limit the material deforms permanently, and finally breaks. Real springs and wires follow F = kx only for small extensions.
A paperclip pulled too far stays bent.
Never extrapolate F = kx for large stretches.
In more detail
Hooke's law holds only up to the elastic limit. Beyond this, the material deforms permanently and the force is no longer proportional to extension.
Real-world uses
- Engineers design components to stay within their elastic limit.
- Crash testing examines how structures deform beyond elastic behaviour.
- A paperclip bent back and forth eventually breaks, because it has been pushed beyond its elastic limit.
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Frequently asked questions
What happens beyond the elastic limit?
The spring or material is permanently deformed and may not return to its original length.
Does Hooke's law always apply?
Only in its linear range, for small deformations of many materials.
What happens after the elastic limit?
The material deforms permanently, so it does not return to its original shape when the load is removed.
Related topics in Newton's Laws & Forces
Terminal velocity of a sphere · Spring force · Springs in series and parallel · Equilibrium of concurrent forces · Torque and equilibrium · Center of mass