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# When is E ∝ x and when is E ∝ x^2?

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1. E = elastic potential energy.
x = extension.

I know how to derive these, it's from a graph of F-x.

E = 1/2Fx, and E = 1/2kx^2.

And these mean: E ∝ x or E ∝ x^2.

But how do I know when to use each one.
2. (Original post by BrainJuice)
E = elastic potential energy.
x = extension.

I know how to derive these, it's from a graph of F-x.

E = 1/2Fx, and E = 1/2kx^2.

And these mean: E ∝ x or E ∝ x^2.

But how do I know when to use each one.
E = 1/2Fx means energy is proportional to the product of both force and extension... but a given amount of extension implies a given force (Hookes law). force and extension are not independent of each other.
3. (Original post by Joinedup)
E = 1/2Fx means energy is proportional to the product of both force and extension... but a given amount of extension implies a given force (Hookes law). force and extension are not independent of each other.
Thanks.

So you're saying that force is not a constant so E is not directly proportional to x?
4. I think E is directly proportional to x, but only when F is constant.
5. (Original post by BrainJuice)
I think E is directly proportional to x, but only when F is constant.
Constant F means constant x... you cannot vary them independently
-----
F=kx [Hooke's law]

E=1/2 Fx
[sub in Hookes law for F]
E=1/2 (kx) x

E=1/2 kx2

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