Define potential enrgy of a body .Find an expression for the potential energy of a stretched spring.

Explanation

Fig. shows three different states of-spring.
i) Normal state: It is a state, when no external force is applied on the spring.
ii) Stretched/Compressed state
When external.force (`vecF_(en)`) is applied on spring,
In Fig.
`vecF` = Restoring force and `vecx` = .Displacement of spring.
From Hooke.s law, `vecF prop -vecx " or " vecF = - kvecx " " ....(i)`
Since, `vec(F)_("ext") - vecF` so `vecF_("ext") = kvecx`
Total work done to stretch or compress the spring through a distance x is given by
`int dW = intFdx = int_0^x kxdx " or " W = k [(x^2)/(2)]_0^x = 1/2 kx^2`
This work done is stored in the spring as P.E. i.e `U = W = 1/2 kx^2`