Hooke's Law

In mechanics and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law is a useful approximation are known as linear-elastic or "Hookean" materials. Hookean materials is a necessarily broad term that may include the work of muscular layers of the heart. Hooke's law in simple terms says that stress is directly proportional to strain. Mathematically, Hooke's law states that

where

x is the displacement of the spring's end from its equilibrium position (a distance, in SI units: metres);

F is the restoring force exerted by the spring on that end (in SI units: N or kg·m/s2); and

k is a constant called the rate or spring constant (in SI units: N/m or kg/s2).

When this holds, the behavior is said to be linear. If shown on a graph, the line should show a direct variation. There is a negative sign on the right hand side of the equation because the restoring force always acts in the opposite direction of the displacement (for example, when a spring is stretched to the left, it pulls back to the right).

Hooke's law is named after the 17th century British physicist Robert Hooke. He first stated this law in 1660 as a Latin anagram, whose solution he published in 1678 as Ut tensio, sic vis, meaning, "As the extension, so the force".