Linear and angular momentum problem: Ball hitting a rod

[barryj]

Is the angular equation above the same as
m_bv_bd = I_rω_r where d is the distance between the axis of rotation and the impact point?

 

[PeroK]

Is the angular equation above the same as
m_bv_bd = I_rω_r where d is the distance between the axis of rotation and the impact point?

Yes. This assumes, of course, that the ball is at rest after impact.

 

[barryj]

Can I make the statement that the ball comes to rest after impact? If so then the equation in post 42 and 52 are correct, yes? and we can solve for the final v_r and ω_r.

 

[PeroK]

Can I make the statement that the ball comes to rest after impact? If so then the equation in post 42 and 52 are correct, yes? and we can solve for the final v_r and ω_r.

You can assume that is the case. That gives you a specific problem to solve.

Or, you can assume it does not, and that gives you a more general problem to solve.

I had assumed that the source of this question would have made that clear?

 

[barryj]

Perok. Since I set initial parameters for the problem, i.e. elastic collision, masses, velocity of the ball, length of rod, distance of impact from the COM, then I do not think I can assume that the ball will be stationary after impact. Isn't this correct? So if it is not stationary, then many if not all of my equations are incorrect. yes?

 

[PeroK]

Perok. Since I set initial parameters for the problem, i.e. elastic collision, masses, velocity of the ball, length of rod, distance of impact from the COM, then I do not think I can assume that the ball will be stationary after impact. Isn't this correct? So if it is not stationary, then many if not all of my equations are incorrect. yes?

If this is some problem you made up and you want to assume specific numbers for the variables, then you cannot assume the final velocity of the ball is zero.

 

[barryj]

If we assume the ball is stationary after the collision, then as I think you pointed out earlier, then there must be some relationships between the masses of the objects such that KE is also conserved, assuming an elastic collision. Is this correct?

 

[PeroK]

If we assume the ball is stationary after the collision, then as I think you pointed out earlier, then there must be some relationships between the masses of the objects such that KE is also conserved, assuming an elastic collision. Is this correct?

I seem to recall saying that a number of times.

 

[barryj]

I have a thick skull.

 

[barryj]

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?

 

[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