How does the conservation of momentum explain this?

In summary, 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 as the rock goes up and down, with a much smaller distance due to its larger mass.
  • #1
zeromodz
246
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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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  • #2
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.
 
  • #3
The Earth moves
 
  • #4
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.
 
  • #5
As the rock goes up and down, the Earth goes down and up, by a much smaller distance of course.
 

Related to How does the conservation of momentum explain this?

1. How does the conservation of momentum explain the trajectory of a projectile?

The law of conservation of momentum states that the total momentum of a system remains constant, unless acted upon by an external force. In the case of a projectile, the initial momentum is imparted by the force of the launch, and as the projectile travels through the air, there are no significant external forces acting on it. This means that the momentum of the projectile remains constant, resulting in a parabolic trajectory.

2. How does the conservation of momentum explain the recoil of a gun?

When a gun is fired, the gunpowder inside the cartridge explodes, creating a high-pressure gas that pushes the bullet out of the barrel. As the bullet moves in one direction, the gun recoils in the opposite direction, as per Newton's third law of motion. This is possible due to the conservation of momentum, as the total momentum of the system (gun + bullet) must remain constant.

3. How does the conservation of momentum explain the functioning of a rocket?

A rocket works by expelling exhaust gases at high speeds in one direction, which creates an equal and opposite force in the opposite direction, propelling the rocket forward. This is possible due to the conservation of momentum, as the momentum of the exhaust gases is equal and opposite to the momentum of the rocket.

4. How does the conservation of momentum explain the collision between two objects?

During a collision between two objects, the total momentum before the collision is equal to the total momentum after the collision, as long as there are no external forces acting on the system. This is because momentum is conserved, meaning that it cannot be created or destroyed. Therefore, the combined momentum of the two objects before the collision is equal to the combined momentum after the collision.

5. How does the conservation of momentum explain the movement of a pendulum?

A pendulum swings back and forth due to the conservation of momentum. When the pendulum is at its highest point, it has a maximum potential energy and zero kinetic energy. As it swings down, its potential energy is converted into kinetic energy, resulting in an increase in momentum. At the bottom of the swing, the pendulum has maximum kinetic energy and zero potential energy. This process continues, with the total momentum of the pendulum remaining constant throughout its motion.

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