# Hooke's Law

## Physical Law

Hooke's Law applies to an ideal spring:

$\mathbf F = -k \mathbf x$

where:

$\mathbf F$ is the force caused by a displacement $\mathbf x$
$k$ is the spring force constant.

The negative sign indicates that the force pulls in the opposite direction to that of the displacement imposed.

The strain is proportional to the stress.

### Application to Physical Body

While Hooke's Law is exact only when applied to an ideal spring, it also applies, up to a certain stress, to an actual physical body.

### Stress-Strain Diagram

Let the stress on $\BB$ be plotted on the $x$-axis of a graph with the strain caused by the stress plotted against the $y$-axis.

The resulting graph is called a stress-strain diagram.

The above diagram shows a typical graph of stress against strain.

The segment $OA$ represents the region in which Hooke's Law actually applies.

The slope of $OA$ is the modulus of elasticity of the material of which the body is composed.

## Source of Name

This entry was named for Robert Hooke.