Hook's Law

Hooke's law:

Hooke's law: the force is proportional to the extension

Manometers are based on Hooke's law. The force created by gas pressure inside the coiled metal tube at right unwinds it by an amount proportional to the pressure.

The balance wheel at the core of many mechanical clocks and watches depends on Hooke's law. Since the torque generated by the coiled spring is proportional to the angle turned by the wheel, its oscillations have a nearly constant period.

Hooke'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. The law is named after 17th century British physicist Robert Hooke. He first stated the law in 1660 as a Latin anagram.^[1][2] He published the solution of his anagram in 1678 as: ut tensio, sic vis ("as the extension, so the force" or "the extension is proportional to the force").

Hooke's equation in fact holds (to some extent) in many other situations where an elastic body is deformed, such as wind blowing on a tall building, a musician plucking a string of a guitar, or the filling of a party balloon. An elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean.

Hooke's law is only a first order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. In fact, many materials will noticeably deviate from Hooke's law well before those elastic limits are reached.

On the other hand, Hooke's law is an accurate approximation for most solid bodies, as long as the forces and deformations are small enough. For this reason, Hooke's law is extensively used in all branches of science and engineering, and is the foundation of many disciplines such as seismology, molecular mechanics and acoustics. It is also the fundamental principle behind the spring scale, the manometer, and the balance wheel of the mechanical clock.

The modern theory of elasticity generalizes Hooke's law to say that the strain (deformation) of an elastic object or material is proportional to the stress applied to it. However, since general stresses and strains may have multiple independent components, the "proportionality factor" may no longer be just a single real number, but rather a linear map (a tensor) that can be represented by a matrix of real numbers.