How can momentum be conserved in an inelastic collision?

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Discussion Overview

The discussion revolves around the conservation of momentum in the context of inelastic collisions, particularly focusing on the behavior of a ball dropped from a height and its interaction with the ground. Participants explore the implications of momentum and kinetic energy during the collision process.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes dropping a 5kg ball from 2 meters, calculating its impact velocity and questioning how momentum can be conserved if kinetic energy is lost during the collision.
  • Another participant asserts that while the momentum of the ball alone is not conserved due to a change in direction, the total momentum of the ball and Earth system is conserved.
  • A later reply emphasizes that the Earth gains momentum from the collision, which balances the momentum before and after the impact, referencing Newton's 3rd Law.
  • Another participant expresses confusion about the relationship between elastic/inelastic collisions and momentum conservation, clarifying that these terms relate to energy conservation rather than momentum.

Areas of Agreement / Disagreement

Participants generally agree that the total momentum of the ball and Earth is conserved, but there is some confusion regarding the implications of inelastic collisions and the relationship between momentum and energy conservation.

Contextual Notes

There are unresolved assumptions regarding the definitions of elastic and inelastic collisions and their implications for momentum and energy conservation. The discussion does not reach a consensus on the interpretation of these concepts.

pyman12
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Say I drop a ball of mass 5kg from a height of 2 meters, assuming no air resistance, it will hit the ground with a velocity of 6.26m/s and collide with the ground, and rebound. From the law of conservation of momentum, 6.26 * 5 = v * 5, where v is the new velocity of the ball. But if the ball has lost kinetic energy, then through Ek = 0.5 * 5 * v^2, doesn't this mean the velocity of the ball has decreased? And as a result, it is impossible for momentum to be conserved?
 
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pyman12 said:
Say I drop a ball of mass 5kg from a height of 2 meters, assuming no air resistance, it will hit the ground with a velocity of 6.26m/s and collide with the ground, and rebound. From the law of conservation of momentum, 6.26 * 5 = v * 5, where v is the new velocity of the ball. But if the ball has lost kinetic energy, then through Ek = 0.5 * 5 * v^2, doesn't this mean the velocity of the ball has decreased? And as a result, it is impossible for momentum to be conserved?
The total momentum of ball & Earth is conserved. The momentum of the ball alone isn't conserved even if it rebounds with the same speed, because the direction of momentum changes.
 
A.T. said:
The total momentum of ball & Earth is conserved. The momentum of the ball alone isn't conserved even if it rebounds with the same speed, because the direction of momentum changes.

So the Earth has also gained some momentum as a result from the collision, thus balancing the momentum before and after the impact? That makes sense, thanks.
 
pyman12 said:
So the Earth has also gained some momentum as a result from the collision, thus balancing the momentum before and after the impact?
Yes, that is basically what Newtons 3rd Law is about. There are equal but opposite forces on Earth & ball. So the changes in their momentum are also equal but opposite. Hence the total momentum doesn't change.
 
I am puzzled by your question, "How can momentum be conserved in an inelastic collision". "Elastic" or "inelastic" refers to conservation of energy and has nothing to do with conservation of momentum.
 
HallsofIvy said:
I am puzzled by your question, "How can momentum be conserved in an inelastic collision". "Elastic" or "inelastic" refers to conservation of energy and has nothing to do with conservation of momentum.

That was what I was confused about, but I understand now.
 

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