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.
Also see
- Dimension of Spring Force Constant: the dimension of $k$ is $\mathsf {M T}^{-2}$.
Source of Name
This entry was named for Robert Hooke.
Sources
- 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