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Re: 2D Elastic Collisions



Hi Dan Burns:
1. Any 2-body collision is 2-D.
2. There are 4 momentum components for each body (2 initial and
2 final). Four components can be used to specify the initial conditions
for the collision, leaving 4 to be determined. There are 3 equations, as
you have noted, but there are two additional equations that relate the
kinetic energy of each body to its mass and squared momentum. Specifying
one of the final momentum components then makes the system completely determined.
Regards,
Jack
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I have a student who is bothered by the fact that in a 2D collision
involving 2 masses (one at rest) there are seven variables (2 masses, three
speeds, and 2 directions) and only three equations (x momentum, y momentum,
and energy). This means that even if the three initial conditions are
known, only three of the final four conditions can be determined. This
implies that there are multiple possible outcomes for a specific
experiment. He wants to perform experiments to learn about this puzzle. Can
anyone shed light on this problem. Our Halliday, Resnick and Walker text
just says that one of the final conditions must be known.
*******************************************

"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography