Re: The concept of potential energy.

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

I was objecting to what Dario posted on the basis of it being
"too advanced". Otherwise it was appropriate in the context
of our fictitious world of two forces, m*g and k*x.
Ludwik Kowalski

"John S. Denker" wrote:

> At 04:18 PM 10/12/01 -0500, Dario Moreno wrote:
>
> >  ... when somebody talks about "potential energy", what comes
> > to my mind is the definition of potential energy.
> >
> >          (To avoid subscripts, allow me to write U instead of PE.)
> >
> >   What is U, then?  I was thaught that
> >
> >          "The so called potential energy, is a scalar function U(x,y,z)
> > that has the following property: grad U = - force."             (eq 1)
>
> This is not right.
>
> For starters, what if we have a non-conservative force?  How then to
> interpret equation (1)?  There are lots of non-conservative forces in the
> world; a charge subjected to a time-varying magnetic field will suffice as
> an example.
>
> Writing equation (1) seems to deny the existence of non-conservative forces.
>
> >           If we agree that this is a good definition of potencial
> > energy, then it follows that
> >
> >                     Delta  W  =  - grad U dot ds                (eq 2)
>
> Well, we don't agree, we can't say what follows and what doesn't.
>
> Usually the pros write
>                  W = force dot dx                                (eq 3)
> and since -grad(U) is _not_ generally equal to the force, eq (3) is not
> equivalent to eq(2).
>
> >             As you see, it will be very difficult to isolate  the
> > analysis of the notion of potential energy and the notion of work.
>
> I completely disagree.  Suppose I do work (F dot dx) on a free particle,
> imparting energy to it.  Suppose all the energy winds up as _kinetic_
> energy in the particle.  In this case there is complete "isolation" of work
> and potential energy.