## Summary

- The change in size or shape of an object is called deformation and the force applied that causes these changes is called a deforming force.
- If a material tends to return to its original size and shape after a deforming force is applied and then removed, the material is said to be elastic (steel, for example).
- If a material tends to deform permanently after a deforming force is applied and then removed, the material is said to be plastic (wet clay, for example).
- If a material tends to fracture while a deforming force is applied, the material is said to be brittle (concrete, for example).
- All solid materials are elastic as long as the deforming force is less than the elastic limit for the material.

- A spring is…
- a mechanical device whose function depends primarily on it having elastic properties
- a component in a machine used to apply a known force or to store energy
- typically made of coiled steel

- Hooke's law for springs…
- states that the deforming force applied to a spring is directly proportional to its change in length
*F* ∝ ∆*x*

- can be written as the equation
*F* = −*k*∆*x*

where
*k*
- is known as the spring constant (because it is a quantity that varies between springs)
- has the SI unit newton per meter [N/m] but variants like the newton per centimeter [N/cm] or newton per millimeter [N/mm] are also common

- ∆
*x* = *x* − *x*_{0}
- is the change in length of the spring from its equilibrium length, relaxed length, or natural length
*x*_{0} to some new length *x*.
- is described as an extension or elongation when
*x* > *x*_{0}
- is described as a compression or contraction when
*x* < *x*_{0}

- the negative sign indicates that spring exerts…
- a force that acts in direction opposite that of the length change
- a restoring force that acts to restore the spring to its equilibrium length

- is reasonably valid for many springs and other elastic objects over some range of forces and length changes

- The elastic potential energy (
*U*_{s}) of a spring that obeys Hooke's law is given by the equation…
*U*_{s} = ½*k*Δ*x*^{2}