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

Related questions
See all questions in Elastic Collisions
Impact of this question
2085 views around the world
You can reuse this answer
Creative Commons License