[Phys-l] elastic, or not, or both, or neither????

[John Denker <jsd@av8n.com>]

On 10/16/2006 04:29 PM, David Bowman wrote:

> there
> can be a net transfer of kinetic energy from the spacecraft to the
> planet or from the planet to craft

Here's another example of the same thing.  It may be slightly simpler
for the naive student to grasp ... and in any case it is more seasonal!

Consider the interaction of a baseball with a bat.  For simplicity,
neglect the rotational degrees of freedom, and neglect the smallish
irreversible deformation that the ball undergoes.

As a warm-up exercise, we neglect the batter and consider only the
bat and ball.  In the center-of-mass frame, the interaction can be
reasonably well described as an /elastic/ collision.  The ball
and bat just bounce off each other.  Each has the same energy*
before and after.

Things get messy when we realize that in the ballplayers' frame of
reference, there is a very considerable transfer of energy* to the
ball.

This is superficially messy because we have conflict of definitions. 
 -- Those who see "elastic" as "same KE before and after" will classify
  this as an inelastic interaction in the ballplayers' frame (but
  elastic in some other frame).
 -- Those who see "elastic" as non-deforming and/or non-dissipative
  will see this as elastic in all frames.

Things get even messier when we consider the batter connected to
the bat.  There is no frame in which the batter+bat system interacts
elastically with the ball.  This is a mess because from the ball's
point of view, the interaction is essentially the same.  The ball
just bounces off the bat.  The batter makes it seem like the bat
is somewhat heavier, but there is still /some/ frame where the
ball has the same energy* before and after.

I'm not 100% sure how to deal with this mess, but I think the
following may help:  AFAICT there is a problem with saying that
the _interaction_ is elastic or not.  This is at best a misnomer,
and may also be a genuine misconception.  Instead, we should
speak of the elasticity of the _objects_.  In the example above,
the ball returned to its previous form after being deformed, and
therefore behaved elastically, while the batter+bat system behaved
inelastically.

Note (*):  Notice that I said "energy" not KE in all the critical
places.  As I mentioned in a previous note, it is unnecessary and
AFAICT unhelpful to place too much emphasis on KE.  Energy is
primary and fundamental.

Of course, as Michael E. has pointed out, KE is not a worthless
concept.  We agree that KE is a good concept ... but we also
agree there can be too much of a good thing, and intrinsically
good things can be overused and abused.