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

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Hooke's law[edit]

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[edit]

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

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


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

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

The Young's modulus[edit]

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

Strain energy[edit]

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