A ball with a mass of #4# #kg # and velocity of #6# #ms^(-1)# collides with a second ball with a mass of #8# #kg# and velocity of #- 2# #ms^(-1)#. If #40%# of the kinetic energy is lost, what are the final velocities of the balls?
1 Answer
It helps to mentally imagine what the situation is like. If we take left-to-right as the positive direction, then the
After the collision, the larger mass may be stationary, or moving left-to-right (if it bounces back) with a positive velocity, or moving right-to-left (if it keeps moving in the same direction but more slowly) with a negative velocity.
In this case, momentum is conserved. Kinetic energy is not conserved, but we know how much is lost.
Before the collision:
Momentum:
Kinetic energy:
After the collision:
Momentum will be the same, but we know that 40% of the
Just for simplicity, I will continue to use
We can treat these as a set of simultaneous equations: two equations in two unknowns. Rearranging the first, we can express
We can substitute this into the other equation:
Clearly I have done something wrong at some point, since this is mathematical nonsense. I am requesting that other explainers please check and fix this answer.