When is E ∝ x and when is E ∝ x^2?
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.
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.
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.
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.
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?
I think E is directly proportional to x, but only when F is constant.
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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