How can momentum be conserved in an inelastic collision?

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In an inelastic collision, momentum is conserved when considering the system as a whole, including both the ball and the Earth. While the ball loses kinetic energy and its velocity decreases after rebounding, the total momentum of the ball and Earth remains constant due to Newton's third law, which states that forces between the two are equal and opposite. The discussion clarifies that the terms "elastic" and "inelastic" pertain to energy conservation, not momentum conservation. Thus, despite the ball's energy loss, momentum conservation still holds true in the system. Understanding this distinction resolves the initial confusion regarding momentum conservation in inelastic collisions.
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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