Conservation of Momentum: Falling object

  1. Does a ball falling to earth violate conservation of momentum?
  2. jcsd
  3. arildno

    arildno 11,265
    Science Advisor
    Homework Helper
    Gold Member

    Ask yourself:
    Under what conditions will the momentum of a system be conserved?
    Don't double post.
  4. 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?
  5. arildno

    arildno 11,265
    Science Advisor
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    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.
  6. Overall momentum is conserved for a falling object because the earth gains exactly the same momentum but in the opposite direction.
  7. russ_watters

    Staff: Mentor

    You've created an unrealistic, asymetric scenario: how did the ball get in the air in the first place?
  8. 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?
  9. Doc Al

    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.
  10. 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


    mearthvearth + mballvball = constant

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

    mearthvearth = -mballvball

  11. Conservation of Momentum: rolling objects

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

    ranger 1,663
    Gold Member

    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.
  13. russ_watters

    Staff: Mentor

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