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Elastic Collisions in Two Dimensions
Since the theory behind solving two dimensional collisions problems is the same as the one
dimensional case, we will simply take a general example of a two dimensional collision, and
show how to solve it. Consider two particles,
m
1
and
m
2
, moving toward each other with
velocity
v
1
o
and
v
2o
, respectively. They hit in an elastic collision at an angle, and both particles
travel off at an angle to their original displacement, as shown below:
Figure %: Two particles collide at point A, then move of at angles to their original motion
To solve this problem we again use our conservation laws to come up with equations that we
hope to be able to solve. In terms of kinetic energy, since energy is a scalar quantity, we need not
take direction into account, and may simply state:
v
1o
2
+
v
2o
2
=
v
1f
2
+
v
2f
2
Whereas in the one dimensional problem we could only generate one equation for the
conservation of linear momentum, in two dimensional problems we can generate two equations:
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 Fall '10
 DavidJudd
 Physics

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