What is Hooke's law ?

Question

What is Hooke's law ?

Answer 1

In mechanics, and physics, Hooke's law of elasticity is an approximation that 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.

Hooke's law is named after the 17th century British physicist Robert Hooke. He first stated this law in 1676 as a Latin anagram[1], whose solution he published in 1678 as Ut tensio, sic vis, which means:

“ As the extension, so the force. ”

For systems that obey Hooke's law, the extension produced is directly proportional to the load:

where:

is the distance that the spring has been stretched or compressed away from the equilibrium position, which is the position where the spring would naturally come to rest (usually in meters),

is the restoring force exerted by the material (usually in newtons), and

is the force constant (or spring constant). The constant has units of force per unit length (usually in newtons per meter).

When this holds, we say that the behavior is 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 x displacement (when a spring is stretched to the left, it pulls back to the right).

Answer 2

Hooke's law describes the force exerted by a spring.  The equation is F = k(∆x).

k is the spring constant, which depends on the spring being used.

∆x is the distance that the spring is compressed or stretched.  For example, if a spring's unstretched length is 5m, and it is stretched to 6m, ∆x would be +/-1m depending on your coordinate frame.