A ball with a mass of #2# #kg # and velocity of #5# # ms^-1# collides with a second ball with a mass of #7# #kg# and velocity of #- 4# #ms^-1#. If #40%# of the kinetic energy is lost, what are the final velocities of the balls?
1 Answer
Momentum is conserved, but in this instance kinetic energy is not... but we know how much is lost. The solution is
Explanation:
Let's call the
Momentum before the collision:
Kinetic energy before the collision:
The momentum after the collision will be the same as before, the kinetic energy after the collision will be 60% of the value before (due to the 40% loss):
Momentum after the collision:
Kinetic energy after the collision:
We have two equations in two unknowns, which means we can solve them. Rearrange Equation 1 to find a value for
Substitute into Equation 2:
This is a quadratic equation, which can be solved using the quadratic formula or whichever method your prefer:
This yields the value
Substituting these values into Equation 1 yields:
The possible solutions for
The first is physically impossible, since the ball on the right would be moving faster to the left than the one to the left of it, so the solution is