Impulse for 2 Degree of freedom system

[supernova1387]

I have a question which might be simple.

Suppose we have a 2 degree of freedom system such as a double pendulum which is suspended from the ceiling. Now if the second ball (the lower one) collides with the wall, how can we find the impulse exerted on the ball. I mean do we consider the change in linear momentum JUST for the second ball or do we have to find the center of mass of the system and find the velocity change for the center of mass of the system? Recall that principle of linear momentum states that:

mv1 + Ʃ∫ F*dt= mv2
and the impulse I=Ʃ∫ F*dt

 

[K^2]

It's going to be a little complicated, because the constraint forces will transfer impulse between the two masses and between top mass and ceiling. So neither of these two will give you correct answer. The net impulse transferred by wall and ceiling is going to be the center of mass velocity change. But you can't say how much is each one responsible for without doing further analysis.

 

[supernova1387]

Thank you for the reply. What if we assume the 2 mass system are connected together and to the wall by massless rigid links. In that case I think the impulsive forces between the members will be like internal forces and they will cancel each other. Can we say here that the net impulsive force is equal to the change in velocity of the second ball ( the lower one)? Or do we still have to consider the center of mass for the system?

 

[K^2]

The force between the two masses cancels out if you consider CoM motion, of course. The reason I pointed out existence of that interaction is to make sure you don't think that the impulse transferred from the wall goes to the lower mass only. It is shared between the two masses, but so is the impulse from the ceiling. You still can't say anything without going to specific case. If you know angles of both pendulums, lengths of arms, and assume perfectly elastic collision, then you can solve for constraint forces and find out exactly how much momentum was transferred from the wall and the ceiling.

 

[AlephZero]

Can we say here that the net impulsive force is equal to the change in velocity of the second ball ( the lower one)? Or do we still have to consider the center of mass for the system?

Think about what happens if the rod connecting the two balls is horizontal when the collision occurs. The horizontal component of velocity of both balls is the same, before and after the impulse.

To get the impulsive force on the wall, you have to include the change of momentum of both balls.

 

[supernova1387]

Thank you both for your answers.