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Conservation of Momentum: Falling object

by FZX Student
Tags: conservation, falling, momentum, object
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FZX Student
#1
Jan29-05, 03:26 PM
P: 6
Does a ball falling to earth violate conservation of momentum?
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arildno
#2
Jan29-05, 03:42 PM
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Ask yourself:
Under what conditions will the momentum of a system be conserved?
Don't double post.
FZX Student
#3
Jan30-05, 08:51 AM
P: 6
I'm not quite sure I understand. If momentum of a system is to be conserved then pfinal = pinitial. Meaning m1v1=m2v2. The masses will cancel meaning the velocities have to equal. But they don't. If the ball doesn't hit the ground and is just falling, where is the momentum supposed to be conserved?

arildno
#4
Jan30-05, 08:56 AM
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Conservation of Momentum: Falling object

Do you agree that momentum is ONLY conserved when NO EXTERNAL FORCES act upon the system?

For your ball, it is certainly influenced by an EXTERNAL force, gravity!
So your conclusion should be that this is not a momentum-conserving situation.
Thomas2
#5
Jan30-05, 09:53 AM
P: 118
Overall momentum is conserved for a falling object because the earth gains exactly the same momentum but in the opposite direction.
russ_watters
#6
Jan30-05, 10:05 AM
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You've created an unrealistic, asymetric scenario: how did the ball get in the air in the first place?
FZX Student
#7
Jan31-05, 08:31 AM
P: 6
Consider the ball is in mid-fall, it hasn't hit the ground yet and has not just been released. There are no external forces because gravity is providing the impulse. Is momentum conservered in this case or not?
Doc Al
#8
Jan31-05, 09:26 AM
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Quote Quote by FZX Student
Consider the ball is in mid-fall, it hasn't hit the ground yet and has not just been released. There are no external forces because gravity is providing the impulse. Is momentum conservered in this case or not?
If you take the ball as your system, then gravity is an external force (as arildno stated) and the ball's momentum is not conserved. This is clearly true, as you know the speed of the ball increases.
pmb_phy
#9
Jan31-05, 09:56 AM
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Quote Quote by FZX Student
I'm not quite sure I understand. If momentum of a system is to be conserved then pfinal = pinitial. Meaning m1v1=m2v2. The masses will cancel meaning the velocities have to equal. But they don't. If the ball doesn't hit the ground and is just falling, where is the momentum supposed to be conserved?
Its the total momentum of a closed system that is conserved. Not the momentum of a particle. In your case the particle has a force acting on it and as such the momentum changes. There is no law of physics which states that the momentum of a particle is conserved. The gravitational force changs the momentum of a ball in free-fall. However, as someone explained above, the total momentum of the earth/ball system is conserved. The momentum is therefore

pearth + pball = constant

or

mearthvearth + mballvball = constant

If you start with the ball and the earth initially at rest then the constant = 0 and then

mearthvearth = -mballvball

Pete
cparsons10
#10
Jan15-07, 06:46 PM
P: 1
What about when a ball rolls down a ramp. Is conservation of momentum violated?
ranger
#11
Jan15-07, 07:06 PM
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Quote Quote by cparsons10 View Post
What about when a ball rolls down a ramp. Is conservation of momentum violated?
No it is not. As the object moves down the ramp it gains momentum. But it should also be noted that there is an equally strong force on the earth pulling it towards the ball. The acceleration of the earth caused by the ball's gravity is negligible. Thus one can conclude that the change in momentum of the ball is equal [in magnitude] to the change in momentum of the earth, but in the opposite direction. Therefore the net change of momentum is zero and the law of conservation of momentum holds true.
russ_watters
#12
Jan15-07, 11:34 PM
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Amazing that after 2 years, I know what I was thinking and it wasn't leading in the right direction...


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