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[Phys-L] elastic collisions



I was showing my AP physics class a variety of methods for solving 1-d
elastic collisions and I came across something fun that I had never seen --
I hope it's true.

In the special case where the initial momentum of the two objects adds up
to zero, it's quick to show that the only way for both momentum and energy
to be conserved is for the objects to rebound so that their speeds stay as
they were but in the opposite direction.

If the initial momentum is not zero, you can find the velocity of the
center of mass of the objects and then view the events in a reference frame
that moves at that velocity. In that shifted frame, the momentum will be
zero so the objects just reverse their directions. Then you just have to
translate the results back to the initial reference frame.

OK, so what if you were going to solve a bunch of these...You can generate
a rule that works for either object:

Vafter = 2Vcm - Voriginal

Does this seem right? And is it a rule that everyone but me already knew?

Even if it is true, I am not sure I want to show it to my students. I'm
afraid they will use it mindlessly, but it's the ideas behind it that are
the fun part.

And if it turns out that I am mistaken and this is not true, well then I
probably shouldn't teach it to anyone.