How does the conservation of momentum explain this?

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SUMMARY

The conservation of momentum is illustrated through the interaction between a rock and the Earth when the rock is thrown upwards. When a 0.5 kg rock is thrown, its momentum is not conserved in isolation; however, the combined momentum of the rock and the Earth system remains constant. As the rock ascends and then descends, the Earth experiences an equal and opposite change in momentum, despite its much larger mass, demonstrating that momentum is conserved in the system as a whole.

PREREQUISITES
  • Understanding of Newton's Third Law of Motion
  • Basic knowledge of momentum and its conservation
  • Familiarity with gravitational forces
  • Concept of vector quantities in physics
NEXT STEPS
  • Study the principles of Newtonian mechanics
  • Explore examples of momentum conservation in closed systems
  • Learn about gravitational interactions and their effects on motion
  • Investigate real-world applications of momentum conservation in sports or engineering
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Students of physics, educators teaching mechanics, and anyone interested in understanding fundamental concepts of motion and forces in physical systems.

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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