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

Hooke's law

$F={k\;x}$$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 {1}{gradient}}$

$k={\frac {F}{x}}$$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}{Original\;length}}$$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}}$$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}}$$Young\;modulus={\frac {Stress}{Strain}}$

Strain energy

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