Understanding the Relationship between Spring Constant and Energy

AI Thread Summary
The discussion focuses on the relationship between spring constant and elastic potential energy (EPE). It begins with the formula for EPE, EPE = 0.5kx^2, and compares two springs with different constants, K and 2K. A misunderstanding arises regarding the assumption that the extension (x) is the same for both springs, leading to confusion about the energy calculations. It is clarified that the stiffer spring (2K) will have a smaller extension, resulting in equal energy stored for both springs. The thread concludes with an acknowledgment of the mistake in the energy expression.
ravsterphysics
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Homework Statement



1.JPG

Homework Equations

The Attempt at a Solution



EPE is (0.5)kx^2

Let Y have spring constant of K then X has spring constant of 2K

So EPE of Y is (0.50kx^2 which is E

So EPE of X must be (0.5)2kx^2 which is kx^2 which is 2E? But correct answer is E/2??
 
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It looks like you've assumed that x is the same for both springs. Is that going to be the case?
 
gneill said:
It looks like you've assumed that x is the same for both springs. Is that going to be the case?

Ah, in that case if X has a stiffer spring, 2K, then its extension (x) will only be half, so we'd have (0.5)(2K)(0.5x) so the energy stored is the same for both??
 
ravsterphysics said:
Ah, in that case if X has a stiffer spring, 2K, then its extension (x) will only be half, so we'd have (0.5)(2K)(0.5x) so the energy stored is the same for both??
Check the expression you've just used for the energy. Did you forget something?
 
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gneill said:
Check the expression you've just used for the energy. Did you forget something?

Argh such a silly mistake! Thanks for your help : )
 
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