Linear and angular momentum problem: Ball hitting a rod

[jbriggs444]

I have not seen a problem of this type in any of my physics books. All of the problems I see tend to have the rod fixed to a pivot point and this makes the problem much easier. Can this problem even be solved at all?

Yes. Once you have settled on which variant you are interested in, it can be solved.

I think that three variants are currently on the table:

1. Ball ends at rest. Rod is not anchored. Use conservation of linear and angular momentum to determine final linear velocity and angular velocity of rod.

2. Elastic collision. Rod is not anchored. Use conservation of linear and angular momentum and of kinetic energy to determine final linear velocity and angular velocity of rod and final velocity of ball.

3. Ball ends at rest and elastic collision. Rod is not anchored. Use conservation of linear and angular momentum and of kinetic energy to determine final linear velocity and angular velocity of rod and one additional parameter -- such as the point of impact.

 

[barryj]

Lets start with case #1 above. Given my initial parameters, i.e. Mass of ball = 0.1 kg, mass of rod = 1 Kg,velocity of ball = 10 m/sec, impact 0.4 m from rod center, can we assume the ball will be at rest after the collision. I don't think so.

#2 and #3 might be possible. Which one is the easiest to solve? Let's do that one?

 

[barryj]

I solved #3 with d = 0.866