Hooke’s Law

Hooke's LawHooke’s law is a principle of physics that states that the force needed to extend or compress a spring by some distance is proportional to that distance. That is: where is a constant factor characteristic of the spring, its stiffness.

F = -kX, where k is a constant factor characteristic of the spring, its stiffness.

Hooke's Law

Hooke’s law for a spring is often stated under the convention that F is the restoring (reaction) force exerted by the spring on whatever is pulling its free end. In that case the equation becomes

F= -k X\,

since the direction of the restoring force is opposite to that of the displacement.

In SI units, displacements are measured in metres (m), and forces in newtons (N or kg·m/s2). Therefore the spring constant k, and each element of the tensor \kappa, is measured in newtons per metre (N/m), or kilograms per second squared (kg/s2).

For continuous media, each element of the stress tensor \sigma is a force divided by an area; it is therefore measured in units of pressure, namely pascals (Pa, or N/m2, or kg/(m·s2). The elements of the strain tensor \epsilon are dimensionless (displacements divided by distances). Therefore the entries of c_{ijk\ell} are also expressed in units of pressure.

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