When a body is stretched, work is done against the restoring force (internal force).

**Elastic
energy**

When
a body is stretched, work is done against the restoring force (internal force).
This work done is stored in the body in the form of elastic energy. Consider a
wire whose un-stretch length is L and area of cross section is A. Let a force
produce an extension *l *and further
assume that the elastic limit of* *the
wire has not been exceeded and there is no loss in energy. Then, the work done
by the force F is equal to the energy gained by the wire.

The
work done in stretching the wire by d*l*,
dW = F d*l*

The
total work done in stretching the wire from 0 to *l* is

Substituting
equation (7.12) in equation (7.11), we get

Since,
*l i*s the dummy variable in the
integration, we can change *l to lâ€™ *(not
in limits), therefore

Energy
per unit volume is called energy density, u =

A
wire of length 2 m with the area of cross-section 10^{-6}*m*^{2} is used to suspend a load
of 980 N. Calculate i) the stress developed in the wire ii) the strain and iii)
the energy stored.

Given:
Y = 12 Ã— 10^{10}*Nâ€†m*^{âˆ’2}.

Tags : Properties of Matter , 11th Physics : UNIT 7 : Properties of Matter

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11th Physics : UNIT 7 : Properties of Matter : Elastic energy | Properties of Matter

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