An ideal spring of negligible mass is 12.00 cm long when nothing is attached to it. When you hang a 3.15 kg weight from it, you measure its length to be 13.30 cm. If you wanted to store 10.0 J of potential energy in this spring, what would be its total length? Assume that it continues to obey Hooke's law.

Explanation:

Given:

length of unstrained spring,

mass attached to the spring,

length of the spring after hanging the mass,

energy to be stored in the spring,

The length of the spring stretched after hanging the mass:

Therefore the stiffness constant of the spring:

where

F = is the force to which the spring is subjected for the corresponding change in length .

here,

As we know that the spring  potential energy is given as:

where

extension in the length of the spring

So the total length of the spring when it stores 10 J energy:

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