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Re: Introducing Potential Energy



I first point out that the beauty and usefulness of the WE theorem
rests in the remarkable result that the right hand side
(Delta KE) can be evaluated by looking only at the end points
of the motion - it does not depend on the details of the
motion (eg., how v(t) varies in time).

Wouldn't it be nice if the left hand side (the work integral)
could be so evaluated! Let us explore what properties a
force must have to make this so.
After some discussion, show that the rather natural guess
will work; ie., show that if the work integral is a function
only of the end coordinates, then one can choose a (arbitrary)
reference point and define a scalar "field" - a function which
assigns to each space point a number; which number is (minus)
the work integral evaluated from the reference point to the
space point (the argument of the scalar field U(r) ).
The work integral can then be evaluated as the difference
in values of this scalar "field", etc . . .

Be sure to show that the work integral of such a special
force around a closed path is necessarily zero. Making this
physical motivates the names "conservative" force and
"potential" energy.

Hope this is useful.

Bob Sciamanda sciamanda@edinboro.edu
Dept of Physics sciamanda@worldnet.att.net
Edinboro Univ of PA http://www.edinboro.edu/~sciamanda/home.html