Is more elastic potential energy stored in compression than stretching?

[mr.coon]

Question:

Is more elastic potential energy stored in a spring when the spring is compressed by one centimeter than when it is stretched by the same amount?


my conclusion:

part of the definition in the book states that Elastic Potential Energy is the energy that a spring has by virtue of being stretched or compressed. going off this statement i would say that the answer is NO because the definition makes no differentiation between stretching and compressing. there is also some other discussion in the text that would believe me to believe that the EPE would be the same whether the spring is compressed or stretched. also, there is also only one formula in the book: PE_e= 1/2kx² am i right?

 

[Hootenanny]

Question:

Is more elastic potential energy stored in a spring when the spring is compressed by one centimeter than when it is stretched by the same amount?


my conclusion:

part of the definition in the book states that Elastic Potential Energy is the energy that a spring has by virtue of being stretched or compressed. going off this statement i would say that the answer is NO because the definition makes no differentiation between stretching and compressing. there is also some other discussion in the text that would believe me to believe that the EPE would be the same whether the spring is compressed or stretched. also, there is also only one formula in the book: PE_e= 1/2kx² am i right?

You are indeed correct. One can observe the fact simply by looking at the formula for the potential energy. Here x is the displacement of the spring from its equilibrium position, negative x represents compression, whilst positive x represents extension. Since we are dealing with x², it doesn't matter what the sign of x is, merely the magnitude of x. Mathematically, this means that the energy is an even function.

 

[mr.coon]

thank you Hoot.

i just wanted to make absolutely sure because this question is for some extra credit that i desperately need.