# 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, extension is directly proportional 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.

It can also be represented as $Strain={\frac {Changeinlength}{Original\;length}}$ ## 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, y=mx+c;

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

the maximum extent to which a solid may be stretched without permanent alteration of size or shape.

## Plastic limit

When the stress is sufficient to permanently deform the metal, it is called plastic deformation.