Exploring Momentum Conservation in a Falling Ball and Earth System

[jsmith613]

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?

 

[Infinitum]

The Earth collided with the ball too

 

[jsmith613]

The Earth collided with the ball too

so do you mean the Earth's change in momentum is 2mv?

 

[Infinitum]

The change in Earth's momentum is

$$2M_{earth}V_{earth}$$

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

 

[jsmith613]

The change in Earth's momentum is

$$2M_{earth}V_{earth}$$

Where V_earth 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)

 

[Infinitum]

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.