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Re: PE=mgh

At 09:33 PM 10/19/01 -0400, Ludwik Kowalski wrote:
... most textbooks say that an elevated
object "has a potential energy =m*g*h." Can this be
tolerated in the very first encounter with PE?

That can be very nicely tolerated, on first encounters and otherwise.

The textbook author has obviously made some arbitrary choices, including:
-- an arbitrary choice of reference-level for h=0.
-- an arbitrary choice of the potential at that level (PE=0 at h=0).

Arbitrary is not wrong. The author is 100% free to make those choices. Of
course I am free to write another book that chooses a different reference
point and a different gauge.

What is wrong with being tolerant first and elaborating
on the subject later, most likely in the same course?

There's nothing wrong with that. There's really no choice about
that. It's not even a question about tolerating imperfection or tolerating
less than complete generality. Everything we do is imperfect to one degree
or another. Everything we do covers less than the complete general case.

Our only responsibility is to not over-claim the accuracy and generality of
what we've done. PE=mgh is obviously not the general case; it is however
a perfectly reasonable first-order approximation, more than good enough for
a wide range of applications.