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

AI Thread Summary
The discussion centers on the apparent contradiction between Hooke's Law, F=mg=kx, and the energy calculation, mg=(1/2)x*k. The confusion arises from the assumption that energy can be calculated using a constant force, which is not valid in this context. It is emphasized that the energy formula, E=force x displacement, only applies when the force remains constant throughout the displacement. The conversation suggests that understanding differential calculus may clarify the relationship between force and energy in spring systems. Proper measurement of the spring's displacement is crucial for accurate energy calculations.
tallwallyb
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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?
 
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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.
 
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?
 
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