Understanding the Relationship between Spring Constant and Energy

[ravsterphysics]

Homework Statement

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??

 

[gneill]

It looks like you've assumed that x is the same for both springs. Is that going to be the case?

 

[ravsterphysics]

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??

 

[gneill]

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?

 

[ravsterphysics]

Check the expression you've just used for the energy. Did you forget something?

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