# Collisions Impulse; Balls dropped from same height.

In summary, two balls with the same mass are dropped from the same height and one ball bounces higher than the other after colliding with the ground. The collision is elastic and neglecting air resistance, the mechanical energy of the ball is not conserved. The rigidity of the bodies may account for the difference in kinetic energy loss. If we consider the ball-earth system, mechanical energy may still be conserved. The impulse experienced by each ball is not the same, as one ball undergoes a lower change in momentum. The lost work during the collision is mostly converted into heat within the ball.

## 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?

n/a

## The Attempt at a Solution

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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?

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.

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.

## What is a collision impulse?

A collision impulse is the change in momentum that occurs when two objects collide. It is equal to the force applied over a specific amount of time. In simpler terms, it is the impact or "push" that one object exerts on the other during a collision.

## How is impulse related to collisions?

Impulse and collisions are closely related because impulse is the measure of the change in momentum resulting from a collision. In other words, the impulse of a collision determines how much the momentum of each object involved in the collision will change.

## What factors affect the magnitude of the impulse during a collision?

The magnitude of the impulse during a collision is affected by the mass and velocity of the objects involved. A heavier object or one with a greater velocity will result in a larger impulse during a collision.

## What happens to the impulse when the objects have the same mass and velocity?

If the objects have the same mass and velocity, the impulse during the collision will be the same for both objects. This means that the momentum of each object will change by the same amount, resulting in an equal and opposite force exerted on each object.

## How do balls dropped from the same height experience collisions and impulse?

Balls dropped from the same height experience collisions and impulse when they hit the ground. The impulse of the collision between the ball and the ground will cause the momentum of the ball to change, resulting in a bounce. The height of the bounce will depend on the magnitude of the impulse and the elasticity of the ball and ground.

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