One end of an unstretched vertical spring is attached to the ceiling and an object attached to the other end is slowly lowered to its equilibrium position. If S be gain in spring energy and G be loss in gravitational potential energy in the process, then
This was the problem I was trying to solve. I first did it without the law of energy conservation. For equilibrium position we get, $mg = kx$ (gravitational force balances the spring force at equilibrium)
Putting the value of x in $1/2kx^2$... (where x is the deformation in the spring at equilibrium) I end up with the relation G = 2S (the right answer).
How do I go about applying energy conservation in this situation?
$mgx = 1/2kx^2$ (K.E. not considered as the block is lowered slowly)
This gives S=G as the answer. I know I'm making some error while applying energy conservation.
Is there some non-conservative force acting on the block? In that case we can't apply energy conservation, right? But I can only see the spring force and the gravitational force (and also the force applied by the external agent to slowly lower it). Should I also be considering the force applied by the external agent? If so, how do I go about this?
This problem may be silly but it has been troubling me for quite a while. Any help will be appreciated.
