Question

Derived formula for potential energy in spring during compression and expansion

Answer 1

Answer:

Let a massless Spring be attached to the Wall and let a mass(m) be attached to the other side .(refer figure)

To find potential energy =?

Work done = F.S

s= xm

and F = -Kx (mathematical expression)

But the force here is not constant , therefore we take the average value ie., 1/2 F

» W= 1/2 F.s

or, w= 1/2 (-kx)(x)

or, W = -1/2 (kx^2)

This energy appears as potential energy of spring

Therefore, P.E of spring = 1/2 (Kx^2)

Note: Some may use calculus method in this derivation, which is also correct