Re: [Phys-l] non-conservative --> non-grady ???

[John Denker <jsd@av8n.com>]

On 02/20/2008 08:30 AM, Steve Highland wrote:
> Your capacitor example would work the same even if you left the field on for
> the entire time since the electric field outside the capacitor is zero.

Sure it would "work" as an accelerator, but we would have a 
harder time showing that the KE+PE changed, and was not simply
an exchange of PE for KE.

> I'm not quite sure what the issue is that you are trying to address.  Has
> someone claimed that conservative forces cannot do work?  Of course they
> can.  Gravity pulling a falling ball downward does work on the ball.  If you
> define the ball alone to be your system, then its energy increases as it
> falls.  The ball by itself isn't a conservative system.

1) The issue had to do with changing the _sum_ of KE+PE.

2) The gravitational field is a conservative force-field, according 
 to conventional terminology.  Actually if "the system" is a particle
 moving in a gravitational field *is* a conservative system, according
 to conventional terminology.  It is in fact the canonical example:
   http://scienceworld.wolfram.com/physics/ConservativeSystem.html

 As previously explained, the terms "conservative force-field" and 
 "conservation of energy" are not equivalent, which is a major part 
 of the issue I am addressing, as you can tell from the Subject: line.

> If you enlarge the system to include the ball plus the earth, then you can
> use the fact that gravity is conservative to define a potential energy and
> add it to the kinetic energy to give a total energy for the entire system
> that will be conserved as the ball falls.

But I don't want to "enlarge the system".  I need to apply physics
in general (and conservation in particular) to smallish systems and
subsystems.  A global conservation law is not nearly so useful as a 
local conservation law.  For the next level of detail on this, see
  http://www.av8n.com/physics/thermo-laws.htm#sec-energy-con

> Your charge flying through the capacitor ......

> Clearly this system is not a conservative system.  Extra energy is getting
> in. 

I don't want to get mired in terminology, but actually this *is* a 
conservative system, according to accepted definitions.  As previously
emphasized, /conservation/ is not the same as /constancy/.  In this
system, energy is conserved, but the energy of the system is not
constant.  Energy is transferred across the boundary of the system.

  Conservation of XX means that XX is constant _except_
  insofar as XX flows across the boundary of the system.

  This applies to conservation of energy, momentum, charge, lepton
  number, et cetera.  This is what we mean by conservation.  It is
  related to the idea of continuity of world-lines.
     http://www.av8n.com/physics/conservative-flow.htm


>  Where's that energy coming from?

The energy gained by system #1 (the particle) via force dot Δx is equal 
to the energy lost by system #2 (the battery) via voltage times Δq.






============================

On 02/20/2008 09:15 AM, LaMontagne, Bob wrote:
> > How do you "turn off" the field.

Ah, that's a bug in the original version.  Is the new version better?
  http://www.av8n.com/physics/img48/accelerator.png