Collisions Impulse; Balls dropped from same height.

[AdkinsJr]

Homework Statement

Two balls with the same mass are dropped from the same height. After colliding with the ground, one of the balls "A" bounces higher than the other ball "B." Neglect air resistance.

Is mechanical energy conserved ?
Are they subjected to the same impulse after colliding with the ground?

Homework Equations

n/a

The Attempt at a Solution

[/B]
I'm kind of confused by this problem. For the first question, I assume the balls would hit the ground at the same time and with the same velocity (note the problem does not state anything about an initial velocity, so maybe I'm wrong to assume that, but "dropped" to me kind of implies vi=0) regardless of their masses.

The collision is elastic, usually kinetic energy is conserved for "perfectly" elastic collisions, in this case I suppose some of the kinetic energy of ball B has been transferred to the ground, also for ball "A" but Apparently ball "B" loses more kinetic energy during collision since it doesn't rebound as high. Maybe the rigidity of the bodies could account for that?

The mechanical energy of the ball is not being conserved, and there must of been some transfer of energy and momentum to the ground. Of course, the problem does not specify what the system is, but for anyone of the balls, I do not think mechanical energy is being conserved. But if we're talking about the ball-earth system, wouldn't mechanical energy be conserved? I think so.

For the impulse part of the question, clearly one of the balls has underwent a lower change in momentum. Therefore, I don't think impulse is the same for both of them. I know when objects collide the third law requires impulse to be the same, but the balls aren't colliding with each other. So impulse is not the same right?

 

[mfb]

but "dropped" to me kind of implies vi=0

Sure.

Maybe the rigidity of the bodies could account for that?

Or some other detail - you don't have to know what causes the difference.
Do you know that A loses kinetic energy?

But if we're talking about the ball-earth system, wouldn't mechanical energy be conserved? I think so.

Let the balls bounce a few more times until they stay at the ground. Is the mechanical energy still in the ball-earth system? How does that transfer to the single bounce here?

For the impulse part of the question, clearly one of the balls has underwent a lower change in momentum. Therefore, I don't think impulse is the same for both of them. I know when objects collide the third law requires impulse to be the same, but the balls aren't colliding with each other. So impulse is not the same right?

Right. I think you should also add a direct comparison.

 

[haruspex]

some of the kinetic energy of ball B has been transferred to the ground,

Mostly, the lost work will have been turned into heat within the ball.