A ball with a mass of 2 kg is rolling at 7 m/s and elastically collides with a resting ball with a mass of 4 kg. What are the post-collision velocities of the balls?

1 Answer
Andrea B.
Jan 27, 2017

v1 = -2,33 m/s
v2 = 4,66 m/s

Explanation:

in the elastic collisions remain constant both the total kinetic energy both the momentum. Therefore:
1/2 m1 v1°^2 = 1/2 m1v1^2 + 1/2 m2 v2^2.
m1 v1° = m1 v1 + m2 v2 .
replacing the values in the equation of conservation of momentum, you find:
(1) v1= 7 -2 v2 .
that you put in the equation of conservation of energy.
Resolving the second degree equation, you find:
6v2^2 -28 v2 =0.
then V2=0 not useful and
v2 = 4,66 m/s.
If You put in the (1), you find:
v1= -2,66 m/s i.e. the smaller ball comes back.

If you put the values in the equation of conservation of energy, you find that it is verified

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