Exploring Momentum Conservation in a Falling Ball and Earth System

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Discussion Overview

The discussion revolves around the conservation of momentum in the context of a ball falling towards the Earth and colliding with the ground. Participants explore the implications of momentum changes for both the ball and the Earth, particularly during the collision phase.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions how momentum is conserved when the ball changes direction upon colliding with the floor, noting that the momentum change is 2mv.
  • Another participant humorously asserts that the Earth also collides with the ball, suggesting that this should be considered in the momentum conservation analysis.
  • There is a proposal that the change in Earth's momentum can be expressed as 2M_{earth}V_{earth}, where V_{earth} is the original velocity of the Earth, and this is equated to 2mv.
  • A clarification is made regarding the direction of the Earth's motion, indicating that while it is moving downward, this direction is not strictly defined in the context of the discussion.
  • Participants discuss the assumption that the collision is head-on, which influences the interpretation of the Earth's motion relative to the ball.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of momentum conservation during the collision, with multiple viewpoints presented regarding the Earth's motion and the nature of the collision.

Contextual Notes

There are assumptions regarding the definitions of direction and the simplifications made by neglecting the Earth's rotation and revolution. The discussion does not resolve how these factors influence the overall momentum conservation analysis.

jsmith613
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Momentum conservation?

Consider a ball falling towards the earth. I understand here how momentum is conserved here (ball momentum increases in one direction and Earth momentum increases in the other).
BUT when the ball collides with the floor and it changes direction its momentum change is 2mv. How is momentum consereved in the whole system?
 
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The Earth collided with the ball too :wink:
 


Infinitum said:
The Earth collided with the ball too :wink:
so do you mean the Earth's change in momentum is 2mv?
 


The change in Earth's momentum is

2M_{earth}V_{earth}

Where Vearth is the original velocity with which the Earth was moving(neglecting rotation/revolution), and that is equal to 2mv.
 
Last edited:


Infinitum said:
The change in Earth's momentum is

2M_{earth}V_{earth}

Where Vearth is the original velocity with which the Earth was moving, and that is equal to 2mv.

ok so to check that means the Earth is moving DOWNWARD (however negligible the motion)
 


Pretty much, yes. Though downward isn't exactly defined in this sense. More appropriate to say Earth is moving opposite to the original direction of motion, assuming the collision was head-on.
 

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