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

Hooke's law

$F=kx$

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 gradient refers to the gradient of a Tension-Extension graph.
The standard units of k are N m⁻¹

Strain

$Strain=\frac{Extension}{Originallength}$

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

It can also be represented as $Strain=\frac{Changeinlength}{Originallength}$

Stress

$Stress=\frac{Force}{CrossSectionalArea}$

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

The Young's modulus

$Youngmodulus=\frac{Stress}{Strain}$

Strain energy

$Strainenergy=\frac{1}{2}Fx$

However, due to Hooke's Law, it can be calculated in another form, y=mx+c;

$Strainenergy=\frac{1}{2}2jx=\frac{1}{2}k{x}^2$ Template:A-level physics

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.