Hooke's Law

Hooke's law states the relationship between the force applied to a wire and the extension of the wire. The change in length of the wire is proportional to the change in force.

Hooke's law: F=kx 

F is the force or load in newtons (N)

k is the force constant (or stiffness constant) in newtons per metre (Nm-1)

x is the extension in metres (m)

Hooke's law doesn't only apply to wires, most materials will obey it to a point.

Hooke's Law in Springs

Springs also have a change in extension when a load is applied.

Hooke's law also applies to springs as the extension or compression of a spring is proportional to the load or force applied. Rather than force constant, the k in the formula when applied to springs can be called the spring constant (spring stiffness)

Tensile forces cause the spring to stretch, where as compressive forces squash the spring. Hooke's law can be used for both tensile and compressive forces, the spring constant has the same value in both forces.

Deformation

Elastic - A deformation is elastic until it reaches its elastic limit. When the deformations is elastic, the material returns to its original shape once the load is removed. Atoms can move small distances from their equilibrium position without changing position in the material.

Plastic - A deformation is plastic beyond the materials elastic limit. The material wont return to its original shape once the load is removed, it is permanently stretched. Atoms in the material move relative to each other and don't return to their original positions.

Limit of Proportionality - The greatest force which can be applied to a material for Hooke's law to remain true. Once this limit is exceeded the relationship between force and extension is no longer linear.

Force Extension Graph
 * This is a graph of force against extension for a wire.
 * Where the force and extension have a linear relationship, Hooke's law is being obeyed.
 * Once the limit of proportionality is reached, the graph begins to curve and Hooke's law is no longer applicable.
 * When the elastic limit is exceeded the material will be permanently stretched, once the load is removed the material will be longer.
 * The stiffness constant of the material can be calculated from the gradient of the graph, up to the limit of proportionality.