Young Modulus ~ University Notes

Young Modulus

The value of a Stiffness Constant only applies to a certain sample. For example, a longer piece of the same material would have a lower stiffness constant. The Young Modulus on the other hand is a material property, meaning it can be applied to all samples of the same material. It is calculated by the formula:

$Young\,Modulus=\frac{Stress}{Strain}$ $E=\frac{\sigma}{\varepsilon}$

Stress and Strain

Stress is a measure of the force applied per unit cross-sectional area of a material. It is measured in Pascals (Pa, or Nm^-2, or Kgm^-1s^-2 if you want to be pedantic). It is hence calculated by the formula:

$Stress,\:\sigma=\frac{force}{cross-sectional\;\;area}$

Strain is the change in length relative to original length. It has no units since it is the ratio of two lengths. It is calculated by the formula:

$Strain,\:\vare=\frac{extension}{original\;\;length}$

A stress on a material causes a strain.

For a material, a stress-strain graph can be drawn. The gradient of this graph is then the Young Modulus. The Young Modulus is also measured in Pascals. By finding the area under a stress-strain graph, it is possible to work out the energy stored per unit volume in a material.

http://chart.apis.google.com/chart?http://chart.apis.google.com/chart?&chxl=0:|Stress|1:|Strain&chxp=0,100|1,100&chxs=0,676767,20,0.5,l,676767|1,676767,20,-0.5,l,676767&chxt=y,x&chs=500x300&cht=lxy&chco=000000&chd=s:A9,A9&chls=2&chma=10,0,0,10|10&chm=B,6FDB77BB,0,0,0

The Young Modulus, being a material property as it is, can be used to generalise the elastic properties of a material. This is very useful, for example, in working with seat belts, as it important to be able to calculate how far they will stretch for any length or thickness.

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