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").
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.
