Re: [Phys-l] conservation versus constancy

[John Denker <jsd@av8n.com>]

On 10/16/2006 12:38 PM, Spinoza321@aol.com wrote:

> By definition elastic collisions conserve KE, inelastic collisions don't. 


That "definition" is a new one on me. 

I thought elastic was defined to mean capable of returning to initial form
after being deformed.  That is a far cry from requiring no deformation.
  http://www.yourdictionary.com/ahd/e/e0065500.html

If the forces during the interaction are non-zero and non-infinite, then
some KE *will* be converted to other forms, as Bob pointed out.  This is
an inescapable consequence of the work/KE theorem.

In an elastic collision, some nonzero amount of KE is "borrowed" on the
inbound leg and "repaid" on the outbound leg.

I thought Bob's note was clear, informative, and non-nit-picky.

On 10/16/2006 02:02 PM, Bernard Cleyet wrote:

> > I think it's understood that the application of conservation is to
> > before and after a processes, not during.

That is at best a matter of taste.  Sometimes the far-field black-box
analysis is appropriate ... and sometimes looking at the mechanism
(i.e. looking inside the black box) is appropriate.

There may not even *be* a valid far-field limit, especially if we are
dealing with infinite-range interactions such as gravitation or
electrostatics.

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

I find it unhelpful to focus too much attention on KE.
 ++ There is a grand law of conservation of energy.  Local conservation.
 ++ There is a grand law of conservation of momentum.  Also local.
 ++ There is conservation of phase space, and associated ideas of entropy.
 -- There is no comparable law of conservation of KE.

The point here is that for simple two-body collisions, the idea of
"elastic"
interaction can be perfectly well expressed in terms of energy and momentum.
For more complicated interactions, it may be necessary to say something
about entropy or "dissipation" or the like.

This is not a trivial point, because it allows us to generalize to photons
and other situations where identifying the "kinetic" piece of the energy
is not always convenient.

For structureless particles, such as are used in introductory discussions,
outside the interaction region *all* of the energy is kinetic, so there
can be no advantage to formulating the discussion in terms of KE instead
of simply E.  And E has the advantage of being more fundamental.

> > Otherwise, one may 
> >
> > arbitrarily assign as elastic a collision if, say, 99% of the initial 
> >
> > ... 96% probably more realistic

I've used mechanical oscillators where the deformation was 99.9999+%
elastic.
That is, the Q of the oscillator was well over a million.
  http://www.google.com/search?q=reppy+torsional-oscillator
Part of the job included running up the amplitude to find the elastic limit,
i.e. the onset of inelasticity.