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[Phys-L] Re: Momentum Again



I still think most people are missing the reason for the question about
exactly 1/2 of the KE being transferred in a perfectly inelastic collision
between same mass objects, one at rest.

The question, as I read it, is HOW is exactly 1/2 transferred? Restating
the math of momentum conservation or stating that no real-life situation
actually behaves this way, is not, if I interpret the question properly, an
answer. Here is what I imagine a student thinking:

"A ball is moving along at speed v, has momentum mv, and KE .5mv^2. Now
there is this collision, and after the collision, the math says that only
half of the energy is KE. But where did the rest of the energy go? Heat,
sound, deformation--OK, but HOW does exactly 1/2 of the original energy find
its way into these other channels, none of which are very well defined nor
necessarily exactly the same from collision to collision."

Again, I offer that the problem here is the reification of
energy--considering it to be 'contained' in the first ball and somehow
'flowing out' into these other channels during the collision. In that
model, it is natural to ask 'how does exactly 1/2 remain in the kinetic
channel and half moves into the others?'

I seem to be becoming a JG convert here--but would still have a lot of
trouble dealing this formally with energy in my gen-ed class on world energy
problems. ;-)

Rick

*********************************************************
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, Indiana
rtarara@saintmarys.edu
********************************************************
Free Physics Educational Software (Win & Mac)
NEW: Updated MOTION animations.
www.saintmarys.edu/~rtarara/software.html
Energy 2100--class project
www.saintmarys.edu/~rtarara/ENERGY_PROJECT/ENERGY2100.htm
********************************************************

----- Original Message -----
From: "Bob Sciamanda" <trebor@WINBEAM.COM>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Wednesday, December 07, 2005 10:30 AM
Subject: Re: Momentum Again


In our physics, "WHY questions" are answered within the context of a
mathematical and/or conceptual model.
In the most trivial case the answer involves no more than stating the
definitions of the involved terms:
Ex(1): Why does the ocean meet the land at the shoreline? The answer is
simply to utter the definition of the word "shoreline".

More involved situations can involve adding to the definitions of terms
certain propositions from the appropriate model, which add connections
between the involved terms:
Ex(2): Why is it that a totally inelastic collision between a moving
object
and a stationary object of equal mass necessitates the dissipation of 1/2
the original kinetic energy.
Our model adds to the definitions of terms the conservation of momentum,
and forces:

M*Vi = 2*M*Vf The definition of terms does the rest:

KEf = (1/2)*(2m)*(Vf^2) = (m*Vi^2)/4 =KEi/2

What else can "WHY?" mean to physics?

Addendum:
Note that this mandated transformation of kinetic energy into another form
is not restricted to the totally inelastic collision. A perfectly ELASTIC
collision of these same objects would also necessarily involve the
transformation of kinetic energy into other forms - the difference is that
this transformation is temporary - the mechanism is elastic and the "lost"
kinetic energy is returned to the objects as kinetic energy before the
interaction is over. Again, all of this is "because" of the definition of
terms, logic and our mathematical/conceptual model (Conservation of
Momentum).

PS: Note that the CONS OF MOM is the necessary, added proposition here.
The
definitions, not even the 1/2 in the definition of KE, are not sufficient
"reason" for the result.
If the definition of KE were to be KE = k*M*V^2, (where k is any positive
number) the conclusion would still follow (1/2 the KE is dissipated).

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
http://www.winbeam.com/~trebor/
trebor@winbeam.com
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