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RE: Introducing Potential Energy



John,

Thanks for the response. I hope you will elaborate and others will give
their thoughts and opinions.

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.

I'm well fed from lunch, so let me say what bothers me, John I like your
wording above. I have the same problem whether its calculus or non-calculus
level.


(A) I usually introduce the topic by looking at a moving mass towards a
spring (no friction) and note how the kinetic energy of the mass goes to
zero and then comes back to its original value when the mass loses contact
with the spring, but moving in the opposite direction. (I think the
"reliable word" could be used to good effect here). I then say words to the
effect that we lost the kinetic energy and then reliably got it back. . . .
this is some how associated with the spring force . . . let's give it a name
.. . . potential to recover the energy or potential energy. . . .

(B) I then make the same discussion with a ball tossed straight up near the
surface of the earth in a vacuum.

The discussion in (A) makes feel a little uneasy, because it seems a little
"magical" to me. Although, it does anticipate the discussion a few days
later on the principal of conservation of energy and my reading of Feynman's
blocks story to the class. Perhaps I should read this story first to get
across the idea that potential energy can be thought of as an accounting
device . . .

Discussion (B) causes some uneasy feelings due to a certain lack of
concretness. For the spring it is easy to think in terms of "location" of
the potential energy, in the spring. And most students have no trouble
thinking of the spring having a "potential" to "spring" back. But this kind
of language suffers when dealing with gravity. Again your use of the term
"reliable" would help here as well.

How do others introduce this topic, what are your thoughts, opinions, etc.
for doing so.
Remember, I'm talking about the first day you introduce the concept to
introductory students; which is why my description above is using rather
fuzzy, imprecise terms and is not in terms of minus integral F dot dL.

Joel