Solving Spring Problem w/ Mass of 65.0kg & Force of 775N

[dagger32]

ok, maybe i am missing something here with this problem and it is probably really simple, but here it is:

A force of 775N stretches a certain spring a distance of 0.200m. What is the potential energy of the spring when a mass of 65.0kg hangs vertically from it?

I have tried conservation of energy laws, figuring that the total potential energy of the system is elastic energy + grav. potential energy. I have tried equatng gravtational potential energy to elastic potential energy, which has gotten me nowhere.

My first step was to find k, the spring constant, which I got to be 3875 using Hooke's Law. Yet, the biggest problem I am having is trying to calculate the distance the spring will stretch with this mass. .2 m is not correct because the spring should have a longer distance due to gravity. Hence, i was trying to equate grav. potential energy and elastic potential energy.

I think I am just completely missing something or misinterpreting the problem.

 

[stunner5000pt]

ok draw a free body diagram of the mass hanging from the spring and see your FORCES involved and not the energies, yet

How much is the spring stretched by when the mass is hanging?

Can you calculate the energy stored in the spring given the stretch of the spring?

 

[dagger32]

a little drawing goes a long way. Just had to use the force of weight, find the distance using hookes law, and throw that into the elastic potential energy formula.

Thanks!