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 dl, dW = F dl
The total work done in stretching the wire from 0 to l is
equation (7.12) in equation (7.11), we get
Since, l is the dummy variable in the integration, we can change l to l’ (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 10-6m2 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 × 1010N m−2.