Springs: Force vs. Energy

• tallwallyb
In summary, the conversation discusses the discrepancy between the equations mg=(1/2)*x*k and F=mg=kx, both of which relate to energy and Hooke's law. The speaker asks for clarification on why these equations seem to contradict each other. The conversation also mentions using energy considerations to determine the change in x of the weight, and emphasizes the importance of following a specific procedure in order to do so accurately. The expert suggests that the discrepancy may be due to the force not being constant, and asks if the speaker is familiar with differential calculus.

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?

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.

topsquark
tallwallyb said:
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?

topsquark