Why Does Hooke's Law Seem Contradictory in Calculating Spring Energy?

[tallwallyb]

Homework Statement

Given a vertical spring with spring constant k=53N/m, a 2.5kg weight is hung from it. What is the change in x of the weight. (USE HOOKE'S LAW and compare it to using ENERGY.

Relevant Equations

F = kx
PEs = (1/2)kx^2
PEg = (mgh)

On the energy part, I keep getting mg=(1/2)*x*k, which is contradictory to Hooke's law F=mg=kx. What is going on?

 

[kuruman]

Please show how you applied energy considerations. Suppose you were given the spring and mass and you wanted to measure "the change in x of the weight." What procedure will you follow to do that? That procedure is important because it will inform your use of energy considerations.

 

[haruspex]

On the energy part, I keep getting mg=(1/2)*x*k, which is contradictory to Hooke's law F=mg=kx. What is going on?

I'm guessing you divided E by x expecting to get F. But the equation energy = force x displacement only works if the force is constant.
Are you familiar with differential calculus?