A ball with a mass of #4 kg # and velocity of #9 m/s# collides with a second ball with a mass of #7 kg# and velocity of #- 5 m/s#. If #80%# of the kinetic energy is lost, what are the final velocities of the balls?
1 Answer
This is a relatively complicated collision problem. You won't see many of these unless you're majoring in physics or are an engineer.
By definition, energy is not conserved in this collision, due to the question's statement about kinetic energy being lost.
Therefore, the collision is inelastic and the conservation of momentum is observed, still.
However, given your data we can make a handy approximation,
Where,
Let's start by finding the initial kinetic energy, and recall,
So,
Intuitively, the larger ball will move slower than the faster ball after the collision, even if it is inelastic.
We have two variables, so we need two equations!
Now, remember what we said about conservation of momentum, the momentum after the collision will be the same as before, regardless of the energy lost.
From here on we will use some substitution by defining
Now, let's solve for
Thanks to this answer for providing a push in the right direction for me!
