Re: elastic collisions

["Carl E. Mungan" <mungan@USNA.EDU>]

I'm really late responding to JSD's message (how *do* you folks keep
up with this list anyways?) but I can't resist adding a comment:

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

I agree because the spin energy is internal. But I wonder if I might
tickle your fancy by coining a different idea of an elastic angular
collision. It goes as follows.

An elastic translational collision is one in which linear momentum is
conserved and translational KE is the same before and after. (I'm
reluctant to say the KE is conserved for reasons discussed below.)

So how about defining an elastic angular collision as one in which
angular momentum is conserved and rotational KE is the same?

One example in which this occurs is a planet orbiting the sun.
An amusing tabletop demo of a second example is discussed here:
http://physics.usna.edu/physics/faculty/mungan/Publications/TPT2.pdf

> I am aware that some people, especially in elementary
> texts, use "elastic" as a synonym for "nondissipative"
> but I don't recommend that.

My preference is to define "elastic" to mean mechanical energy is conserved.
HOWEVER, as usual, I do *not* count rotational energy as mechanical.
I define mechanical energy for a set of bulk parts of a system to be
the sum of the translational KE of the parts plus the PE due to
conservative interactions between the parts.

My reason for this definition is that I can then accurately state
that mechanical energy is conserved at all points in time during an
elastic collision, *including during the collision itself*. This is
obviously not true of the KE. The advantage is I can now more easily
explain how to do the standard textbook problem of finding the
compression of the spring bumper of two colliding aircarts.

Also, this definition is consistent with the adjective "elastic" in
that it suggests we are elastically storing up mechanical energy
during the collision.
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu    http://physics.usna.edu/physics/faculty/mungan/

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