An elastic string of unstretched length `l` and force constant `k` is stretched by a small length `x`. It is further stretched by another small length y . The work done in the second stretching is
Elastic force in string is conservative in nature .
`:.` `W = Dela u`
where W = work done by elastic force of string
`Delta u` = Change in elastic potential energy
`because ` ` W = - (u_f - u_i) = u_i - U_f`
or `w = 1/2 kx^2 - 1/2 k(x + y)^2`
or `w = 1/2kx^2 - 1/2 k(x^2 + y^2 + 2xy)`
= `1/2kx^2 - 1/2 kx^2 - 1/2ky^2 - 1/2 K( 2xy)`
= ` - kxy - 1/2 ky^2`
= `1/2 ky( - 2x - y)`
The work done against elastic force is
`w_(external) = - w = (ky)/(2) (3x + y)`
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