Momentum and Impulse Sample Problem Answers

1. A 50kg girl throws a 7kg medicine ball at 10m/s to a 40kg boy. If both are on a frictionless frozen lake, what are both the children's recoil velocities?

girl = -1.40m/s
boy = 1.4894m/s

We need to take this problem in to parts. First, we work with the girl and the ball, and then the boy and the ball. Both sections just use the conservation of momentum equation.

50kg(0m/s) + 7kg(0m/s) = 50kg(v) + 7kg(10m/s)
v = -1.40m/s
40kg(0m/s) + 7kg(10m/s) = 47kg(v)
v = 1.4894m/s

2. A 0.6kg basketball strikes the floor at 6m/s and rebounds at 5.2m/s. If it is in contact with the floor for 0.12 seconds, what is the average force on the ball?

This is just a matter of impulse. Change in momentum equals force times time.

0.6kg(5.2m/s) - 0.6kg(-6m/s) = FNET * 0.12s
FNET = 56N

3. A 0.2kg mass moves in a 0.5m radius circular path with an angular velocity of 2rad/s. What is the new angular velocity of the mass when the string is moving in a 0.2m radius circular path?

This is just another conservation of momentum equation, except that it's angular momentum not linear momentum.

0.2kg(0.5m)^2 * (2rad/s)^2(0.5m) = 0.2kg(0.2m)^2 * ^2(0.2m)
^2 = 62.5rad^2/s^2
= 7.9057rad/s