Re: elastic collisions

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

Jeff Weitz wrote:
...
> elastic collisions, which are usually defined as collisions
> that conserve total kinetic energy, or so I've always thought.

OK for point particles ....

>  Now we have an august textbook that defines elastic collisions
> as collisions in which, "in the cm frame, the velocity changes
> in direction, but not in magnitude."  (p129) Later, in the discussion
> of energy, RHK states that as "an alternate definition of an
> elastic collision: In an elastic collision, the total kinetic
> energy of the two bodies remains constant..."

For point particles, the two definitions are obviously
equivalent.

> This might be a sort of "chicken and egg" quibble

Actually even less exciting than that.
Chickens are different from eggs.  For point particles,
the foregoing shapes up as a six-versus-half-dozen quibble.

> except for the issue of collisions where some of the
> initial translational KE ends up in rotation,

or other internal energy in a non-pointlike particle.

I recommend ducking this issue by declaring that a
collision that imparts spin to the puck is inelastic.

If we were to allow storage of rotational energy to
count as elastic, we would be letting the camel's nose
into the tent.  Here's what the rest of the camel looks
like:  Suppose we have a cart with two onboard flywheels.
(Two, counterrotating, so I don't need to worry about
net angular momentum.)  The cart starts out at rest,
but then uses the flywheel energy to extend a plunger
that pushes against a wall.  The cart goes flying off.
It would be distasteful to me to consider that an
elastic interaction, even though (if you do it right)
it just converts one sort of kinetic energy to
another.

My recommendation is consistent with the usage in
atomic physics, where a collision that leaves one
of the molecules in an excited rotational state is
considered inelastic.

I am aware that some people, especially in elementary
texts, use "elastic" as a synonym for "nondissipative"
but I don't recommend that.  And in particular you
should !!not!! try to come up with an elementary
mechanical definition of nondissipative.  Many people
have tried and failed.  Dissipation depends on entropy.
You can't derive entropy from energy or vice versa.

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.