Over what range of forces is hooke's law obeyed?

Answer 1

Hooke's law only holds for some materials under certain loading conditions. Steel exhibits linear-elastic behavior in most engineering applications; Hooke's law is valid for it throughout its elastic range (i.e., for stresses below the yield strength). For some other materials, such as Aluminum, Hooke's law is only valid for a portion of the elastic range. For these materials a proportional limit stress is defined, below which the errors associated with the linear approximation are negligible.

Materials such as rubber, for which Hooke's law is never valid, are known as "non-hookean". The stiffness of rubber is not only stress dependent, but is also very sensitive to temperature and loading rate.

Applications of the law include spring operated weighing machines, stress analysis and modeling of materials.

Hooke's law:
Hooke's law accurately models the physical properties of common mechanical springs.In physics, Hooke's law of elasticity is an approximation which states that the amount by which a material body is deformed (the strain) is linearly related to the force causing the deformation (the stress). Materials for which Hooke's law is a useful approximation are known as linear-elastic or "Hookean" materials.

For systems that obey Hooke's law, the extension produced is proportional to the load:
F=k.x
where,

x is the distance the spring is elongated by,
F is the restoring force exerted by the spring, and
k is the spring constant or force constant of the spring.
When this holds, we say that the spring is a linear spring.

Hooke's law mathematically comes from the fact that in most solids (and in most isolated molecules) atoms are in the state of stable equilibrium.

For many applications, a prismatic rod, with length L and cross sectional area A, can be treated as a linear spring. Its extension (strain) is linearly proportional to its tensile stress, σ by a constant factor, the inverse of its modulus of elasticity, E.

Answer 2

Its over the range of elastic deformation of the material. Once the material starts to deform plastic ally Hooke's law fails. This point of failure depends on many things, such as the material, how the material was made, its size, shape, etc.

Answer 3

Depends on the system you are approximating. With springs it can be very large or very short, depending on the design of the spring. With hydrogen Hooke's law is also a very good approximation unless you get too close to the atom or to far away: totally depends on the system.

Answer 4

spring forces