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Re: [Phys-l] Interactive Physics Simulations



Regarding Rick's comment:

I maybe haven't read this thread carefully enough, but could someone
define what a 'totally' inelastic collision actually is? In my
mind, an elastic collision conserves both momentum and kinetic
energy while an inelastic collision conserves momentum but not KE.
It's the 'totally' that is confusing me here.

Rick

Rick, I think what is usually meant by the modifier 'totally' in
these discussions is the idea that the collision has the maximum net
permanent consumption of macroscopic translational kinetic energy as
is possible consistent with the momentum conservation requirement.
In this case the final translational kinetic energy of the colliding
objects as seen in the center-of-mass-at-rest frame is zero. So in
that frame *all* the initial kinetic energy was 'totally' consumed.
That's why there is the requirement of sticking or of zero relative
separation speed for that case.

However, it should be pointed out that any collision--neither elastic
nor inelastic of any amount of inelasticity (i.e. coefficient of
restitution) actually conserves kinetic energy. This is because
during the time the collision is happening there invariably a
transfer of kinetic energy into degrees of freedom that are *not*
those of the translational degrees of freedom of the colliding
objects. Typically, during a perfectly elastic collision the amount
of total translational kinetic energy *drops* from its initial value
as some of that energy is moved into the degrees of freedom
describing the *potential* energy of deformation of the colliding
objects. As the collision proceeds to completion (in a perfectly
elastic collision) that potential energy of deformation is fully
moved back into the translational kinetic energy degrees of freedom
of the colliding bodies, and the final total translational kinetic
energy of the objects is the same as their initial translational
kinetic energy before the collision had started. Thus that energy is
*not* conserved; it is merely *restored* to its initial value. If
the translational kinetic energy were actually conserved there would
not have been the temporary drop in its value as some of the energy
went into the potential energy of deformation.

David Bowman