### Energy stored in stretched string

During my course of teaching of elasticity ,i teach about the energy stored in the stretch string.One of the example is a sling in which when rubber string is stretched elastic

#### W = ½ EA/L (DL)

#### W = ½ F (DL)

#### Thus, the elastic energy per unit volume is given by-

#### U = W/AL = ½ stress ´ strain

#### (1) The above results is true for all types of stress and strain.

#### (2) The work done per unit volume or the elastic energy per unit volume is given by half the product of stress and strain.

#### (3) If we draw a graph between stress and strain then as the area between the graph and strain axis is ½ stress ´ strain, it gives the work done per unit volume.

potential energy get stored and when it is released it converts into kinetic energy.

__WORK DONE AND ELASTIC ENERGY__

Let us take the example of a wire. Suppose the original length of the wire is L, When not deformed, there are no internal forces. As the length of the wire increase from L to L + DL, internal forces increase from 0 to F. Suppose at any instant when the length is (L +x), the internal force is F_{x}. The work done to further increase the length through dx is F_{x}dx, hence total work done

W = F_{x} dx = EA/L x dx

So the total work done is

#### W = ½ EA/L (DL)^{2}

#### W = ½ F (DL)

#### Thus, the elastic energy per unit volume is given by-

#### U = W/AL = ½ stress ´ strain

#### (1) The above results is true for all types of stress and strain.

#### (2) The work done per unit volume or the elastic energy per unit volume is given by half the product of stress and strain.

#### (3) If we draw a graph between stress and strain then as the area between the graph and strain axis is ½ stress ´ strain, it gives the work done per unit volume.

There is a beautiful video which the maximum energy which can be given particle which is being thrown with the help of sling

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