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Potential Energy Stored in a Stretched Wire

Potential Energy Stored in a Stretched Wire

↪ Suppose a wire of length L and area of cross-section A is stretched through an extension l.
↪ Then the longitudinal strain in the wire and the tensile stress 

↪ If the wire is stretched through a small extension dl, the elementary work done is

↪ The total work done in stretching the wire through the total extension of length l is obtained by integrating (1) as follows.

↪ This work done is stored as the potential energy in the stretched wire and we denote this by U. That is,

↪ The energy density or potential energy per unit volume is
 energy density = work done or energy/volume