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Curieuse
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Homework Statement
The figure shows an 8.00 kg stone at rest on a spring. The spring is compressed by 10.0 cm by the stone.
What is the spring constant?
Homework Equations
Elastic potential energy= [itex]\frac{k{x^{2}}}{2}[/itex]
Gravitational potential energy= mgh
Spring force F= -kx
The Attempt at a Solution
Okay, so I solved this using a free body diagram and Newton's laws
kx = mg -------------------------------------(1)
So, k=(mg)/x= 784 N/m
And this is the answer, alright!
But then i tried using Energy considerations,
And i did this:
Increase in the elastic potential energy of the spring-stone system = decrease in the gravitational potential energy of the stone-earth system
So, [itex]\frac{k{x^{2}}}{2}[/itex] = mgx
which simplifies to give [itex]\frac{kx}{2}[/itex] = mg -------------------------- (2)
and this is obviously wrong!
Where did i go wrong? Is there some other energy i should've considered?
I ruled out Kinetic energy because the system is stationary.
The half term in the l.h.s of (2) is what is causing the problem, evidently! Please help!
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