How does the conservation of momentum explain this?

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Discussion Overview

The discussion revolves around the conservation of momentum in the context of a rock being thrown straight up from the surface of the Earth in a hypothetical scenario without an atmosphere. Participants explore how momentum is conserved in the rock-Earth system during the rock's motion, particularly at the peak of its trajectory.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions where the momentum of the rock goes when it reaches a velocity of zero at its peak, suggesting a misunderstanding of momentum conservation.
  • Another participant clarifies that while the momentum of the rock alone is not conserved, the momentum of the rock and Earth system is conserved, emphasizing that their momenta sum to a constant value.
  • It is noted that the Earth moves in response to the rock's motion, although the change in Earth's velocity is significantly smaller due to its much larger mass.
  • A later reply reiterates that as the rock ascends and descends, the Earth also experiences a corresponding motion, albeit to a much lesser extent.

Areas of Agreement / Disagreement

Participants generally agree on the principle that the momentum of the rock-Earth system is conserved, but there is some initial confusion regarding the momentum of the rock alone.

Contextual Notes

The discussion assumes a simplified model of the Earth and rock system without atmospheric effects, which may limit the applicability of the arguments presented.

zeromodz
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Picture the Earth without any atmosphere or air molecules. If I were to throw a rock with 0.5 kg straight up from the surface of the Earth it will reach a velocity of zero at its peak? At this moment the momentum of the rock becomes zero. Where does the momentum go if its always conserved?
 
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The momentum of the rock by itself is not conserved. But the momentum of the rock + Earth system is. The vector sum of the momenta of each remains constant throughout the motion.
 
The Earth moves
 
zeromodz said:
Picture the Earth without any atmosphere or air molecules. If I were to throw a rock with 0.5 kg straight up from the surface of the Earth it will reach a velocity of zero at its peak? At this moment the momentum of the rock becomes zero. Where does the momentum go if its always conserved?

The rock has gravitation of its own. As it accelerates toward Earth, reducing its upward speed, Earth also accelerates upward toward it. The velocity change the Earth experiences is far smaller than that experienced by the 0.5 kg mass, but the Earth masses much, much more, so their changes in momentum are equal and opposite.
 
As the rock goes up and down, the Earth goes down and up, by a much smaller distance of course.
 

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