What is Hooke's Law?

Answer 1

It states that within elastic limit the stress is directly proportional to the strain.

Answer 2

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.

Answer 3

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=-kx


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. Hence,

sigma=E*e



Hooke's law is named after the 17th century physicist Robert Hooke.

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.

The most commonly encountered form of Hooke's law is probably the spring equation, which relates the force exerted by a spring to the distance it is stretched by a spring constant, k, measured in force per length.
f=-kx


The negative sign indicates that the force exerted by the spring is in direct opposition to the direction of displacement. It is called a "restoring force", as it tends to restore the system to equilibrium.

The potential energy stored in a spring is given by
U=1/2 * k * x^2


which comes from adding up the energy it takes to incrementally compress the spring. That is, the integral of force over distance. (Note that potential energy of a spring is always positive.)

This potential can be visualized as a parabola on the U-x plane. As the spring is stretched in the positive x-direction, the potential energy increases (the same thing happens as the spring is compressed). The corresponding point on the potential energy curve is higher than that corresponding to the equilibrium position (x=0). The tendency for the spring is to therefore decrease its potential energy by returning to its equilibrium (unstretched) position, just as a ball rolls downhill to decrease its gravitational potential energy.

If a mass is attached to the end of such a spring and the system is bumped, it will oscilate with a natural frequency (or resonant angular (circular) frequency) of

Answer 4

hooke's law states that upto a certain limit
i.e. the elastic limit there is a linear relationship between
the stress and strain .
it means that the graph of stress vrs strain is a straight line upto the elastic limit after which it starts to curve

Answer 5

Hooke's Law refers to the behaviour of elastic bodies. According to this law, the elastic force during an oscillatory movement of an lastic body is given by: F = -kx, where k is the characteristic elasticity of that elastic body, or spring constant, and x is the distance the body is elongated by. It tells us that the elastic force always opposes to any elastic deformation of the body, and that it depends on the body's characteristics and on the enlongation of the body.

Answer 6

The general law of mechanics that stress is directly proportional to strain

Answer 7

HOOKE'S LAW:

STRESS IS DIRECTLY PROPORTIONAL TO STRAIN IN A MATERIAL(ELASTIC) , WITHIN THE ELASTIC LIMIT OF THE MATERIAL.