Hookes law: Calculate the work done by compressing a spring

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SUMMARY

The discussion centers on calculating the work done by compressing a spring using Hooke's Law. The two primary equations referenced are W = Fd and W = 1/2 k x^2. The confusion arises from the application of these formulas; while W = Fd suggests a direct relationship, it fails to account for the variable nature of spring force, which necessitates integration. The correct approach is to use the elastic potential energy equation, W = 1/2 k x^2, as it accurately represents the work done over the distance x.

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Homework Statement


Hookes law: Calculate the work done by compressing a spring by x distance


Homework Equations


W = Fd
Ee = 1/2 k x^2
F = kx


The Attempt at a Solution



I've found two solutions, but only one is correct. I'm confused why it's the second one.

First formula I derived:
W = Fd
F = kx
d = x

Therefore W = kx^2

However, you can also use the elastic potential energy equation which is a modified version of the equation I made which is

W = 1/2 k x^2 - 0

So, why is it the second equation and not the first one? The way I see it, they sort of both are valid. What is wrong with the first one? Work is force * distance, and that's exactly what I'm doing.
 
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The spring force is a function of x, so W = Fd is not valid. You will have to do an integral.
 

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