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# Re: conservative forces +- non-dissipative forces

• From: "John S. Denker" <jsd@MONMOUTH.COM>
• Date: Sat, 30 Jun 2001 13:30:04 -0400

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.