2 Physics Problems?

Question

1)Assume a 9 kg bowling ball moving at 2 m/s bounces off a spring at the same speed that it had before bouncing..
a)What is its momentum of recoil?
b) What is its change in momentum?
c)f the interaction with the spring occurs in 0.5 s, calculate the average force the spring exerts on it.

2) A group of playful astronauts, each with a bag full of balls, form a circle as they free-fall in space. Describe what happens when they begin tossing balls simultaneously to one another.

Answer 1

Question 1
a. The momentum of the ball is 18 kg-m/s. Since it doesn't lose any velocity once it hits the spring, it recoils with the same momentum, 18.

b. I'm not sure which answer they are looking for, but you could either say 0 or 36. 0 would be valid if you are looking for the total momentum of the system (conservation of momentum). The ball's momentum is 18 both before and after it hits the spring. I would also say 36 if you consider the direction of the momentum. Let's say left to right movement is positive. When the ball is travelling right to left, you can say it has a momentum of +18. When it changes direction, the ball has a value of -18:
(+18) - (-18) = +36

F = dp/dt dp=36, dt=0.5

Question 2
There is no gravity in space, so the whole system (balls and astronauts) just move along at a constant velocity. The balls they throw back and forth will also move with constant velocity without falling. Some of the balls will hit each other and begin to bounce off in different directions. Also, the astronauts each use a little bit of force each time they catch and throw a ball. That will move the astronaut slightly and they will each move off into different directions. The longer they do this, the further apart the astronauts will become and the more balls will be floating off in every direction.