Hooke's Law
- A Law stating that, in a linear system, the restoring force is proportional to the displacement of the body, acting in a direction as to restore equilibrium.
- where
- F = restoring force [N]
- k = spring constant [Nm^{-1}]
- x = elongation of material [m]
A material such as copper, when stretched beyond it's elastic limit it retains it's shape.
A material such as rubber, this does not follow Hooke's law and remains elastic until it snaps.
A material such as glass, this follows Hooke's law until it snaps.
The constant of that proportionality is the Young modulus of elasticity for that substance.
- where
- E = Young's modulus [Nm^{-2}]
- F = applied load [N]
- A = cross-sectional area [m^{2}]
- x = extension [m]
- L = original length [m]
- Stress-Strain curve for a material such as mild steel.
- Hooke's Law would apply within the linear region up to the elastic limit of the material.
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See also: Elasticity, Force, Simple Harmonic Motion, Spring Constant, Strain, Stress.
Subjects: Mechanical Engineering