Re: conservative forces +- non-dissipative forces

["John S. Denker" <jsd@MONMOUTH.COM>]

At 12:52 PM 6/30/01 -0400, Geoff Nunes wrote:

> Really, there is no such thing as a "non-conservative" force.

I completely disagree!

> As far as we know, all four fources in nature (gravity, electromagnetism,
> strong, and weak) are completely conservative.

I completely disagree!  See examples below.

I'm not sure where this is coming from, but here are some hypotheses:

 -- People have heard that such-and-such force of nature is described by a
potential.  They seem to forget that not all forces are in this category.
 -- People have heard that the force derived from a potential is
conservative.  They seem to forget the proviso that such a force is
conservative PROVIDED the potential doesn't move!!!!!

A stone is held into the basket of a catapult by forces that would be
conservative _if_ the basket didn't move.  But the basket does move, and it
does work on the stone.

> If the energy goes into making things hot, as with
> sliding friction, then we call it "non-conservative."

Sorry, that's not what is meant by conservative in this context.  That is
the criterion for being _dissipative_ or not.  Being _conservative_ or not
is a separate question.

Examples:
 -- In an ideal roller-coaster, the track provides a force of constraint,
which is conservative (and therefore nondissipative).
 -- In an undamped mass-on-a-spring oscillator, the spring provides a
force that is nondissipative, but not conservative.
 -- A moving potential such as a catapult is non-conservative.
 -- A charged particle in a changing magnetic field is subject to a
non-conservative force.  The equation
        V = phi dot
is a law of nature.  The corresponding force is not the gradient of any
potential.  It is not dissipative.
 -- Any dissipative process is necessarily non-conservative.