Hooke's Law

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Physical Law

Hooke's Law applies to an ideal spring:

$\mathbf F = -k \mathbf x$


$\mathbf F$ 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.

Also see

Source of Name

This entry was named for Robert Hooke.