A-level Physics/Forces and Motion/Deformation of solids

Hooke's law

$F = {k\;x}$

This applies to an object's deformation only before the elastic limit; from then on it deforms plastically and no longer follows this law. it states that,extention is directly propotional to the applied force.

Spring Constant

$k = \frac{1}{gradient}$

$k = \frac{F}{x}$

The standard units of k are N m-1

Strain

$Strain = \frac{Extension}{Original\; length}$

Because this is a division of two measurements of length, Strain has no units and remains a ratio.

Stress

$Stress = \frac{Force}{CrossSectional\; Area}$

The units for Stress are N m-2, otherwise known as Pascals (Pa)

The Young's modulus

$Young \; modulus = \frac{Stress}{Strain}$

Strain energy

$Strain \; energy = \frac{1}{2}Fx$

However, due to Hooke's Law, it can be calculated in another form;

$Strain \; energy = \frac{1}{2}2jx = \frac{1}{2}kx^2$