# Conservation of Momentum: Falling object

1. Jan 29, 2005

### FZX Student

Does a ball falling to earth violate conservation of momentum?

2. Jan 29, 2005

### arildno

Under what conditions will the momentum of a system be conserved?
Don't double post.

3. Jan 30, 2005

### 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?

4. Jan 30, 2005

### arildno

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.

5. Jan 30, 2005

### Thomas2

Overall momentum is conserved for a falling object because the earth gains exactly the same momentum but in the opposite direction.

6. Jan 30, 2005

### Staff: Mentor

You've created an unrealistic, asymetric scenario: how did the ball get in the air in the first place?

7. Jan 31, 2005

### 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?

8. Jan 31, 2005

### Staff: Mentor

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.

9. Jan 31, 2005

### pmb_phy

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

10. Jan 15, 2007

### cparsons10

Conservation of Momentum: rolling objects

What about when a ball rolls down a ramp. Is conservation of momentum violated?

11. Jan 15, 2007

### ranger

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.

12. Jan 15, 2007

### Staff: Mentor

Amazing that after 2 years, I know what I was thinking and it wasn't leading in the right direction... :grumpy: