Are spring potential energy and internal energy the same?

on2t1inf8b

on2t1inf8b

Answered question

2022-07-16

From classical mechanics, the force on a spring is given by the negative gradient of the potential energy with respect to position or displacement.
Can we also say F = U / x, where U is the "internal" energy of the spring?

Answer & Explanation

sweetwisdomgw

sweetwisdomgw

Beginner2022-07-17Added 20 answers

The relation you have stated, F = U / x is valid for all potentials in 1D to determine the conservative force associated with the potential. Note that in the more general case we have the following (for any dimension):
F = U
Where is the gradient operator. Note that the force arises due to a gradient or difference in the potential in space, not due to a changing potential in time. Therefore, temperature would be implicitly included since either T = c o n s t everywhere or T = T ( r ) changes in space in which case the gradient captures the change.

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