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I'm about ready to start introducing potential energy in my
introductory class: I always feel a bit uncomfortable with how I do it.
Let's start a discussion thread on how various people do this.
A quick thought: Especially for non-calculus classes, I have often
introduced potential energy in terms of the work done by what I call
"reliable forces"--forces that can be *relied* on to do some work one way
and an equal but opposite work the other way, forces that can be *relied*
on to do the same amount of work regardless of the path from A to B.
Of course, "reliable" is just another word for "conservative," but I think
it is a far more apt description of the property that we are interested
in. It doesn't take much effort to convince students that gravity and
spring forces are reliable while friction and random pushes and pulls are
not.