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fee6

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## Homework Statement

A stone of mass [tex]m[/tex] is at rest on a vertical spring which is compressed a distance [tex]x[/tex]. Find its spring constant [tex]k[/tex].

All variables are given in the problem.

## Homework Equations

I solved this problem realizing that because the mass is at equilibrium, the sum of the vertical forces on it is 0. Thus, the force of gravity downwards is equal to the force of the spring upwards, and so [tex]mg = kx[/tex].

## The Attempt at a Solution

Therefore, [tex]k = \frac{mg}{x}[/tex], from the previous equation. The problem, now, is that after solving it like this, a friend asked me why we could not use the conservation of energy:

[tex]E_i = E_f[/tex]

[tex]mgx = \frac{1}{2}kx^2[/tex]

[tex]k = \frac{2mg}{x}[/tex]

which differs from the previous solution. I am inclined to believe that there is something wrong with the energy method, but I cannot put my finger on it. I would greatly appreciate any help with this. Thanks!