Hooke's Law

Physical 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.

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

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 actually applies.

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

Dimension of Spring Force Constant: the dimension of $k$ is $\mathsf {M T}^{-2}$.

This entry was named for Robert Hooke.

1966: Isaac Asimov: Understanding Physics ... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $4$: Gravitation: The Gravitational Constant
1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): elasticity
1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Hooke's law
2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): elasticity
2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hooke's law
2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Hooke's law
2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Hooke's law