How Does Momentum Conservation Affect Sled Speed When Susan Jumps On and Off?

[gkangelexa]

Homework Statement

An empty sled is sliding on frictionless ice when Susan drops vertically from a tree above onto the sled. When she lands, does the sled speed up, slow down, or keep the same speed?
The sled slows down.
Later, susan falls sideways off the sled. When she drops off, does the sled speed up, slow down, or keep the same speed?

The Attempt at a Solution

I would think that when she falls off the sled, the speed of the sled should increase because m₂ got smaller, so to conserve momentum, v₂ should get larger
m₁v₁ = m₂v₂


however, the answer is that the sled keeps the same speed... why?

 

[PeterO]

Homework Statement

An empty sled is sliding on frictionless ice when Susan drops vertically from a tree above onto the sled. When she lands, does the sled speed up, slow down, or keep the same speed?
The sled slows down.
Later, susan falls sideways off the sled. When she drops off, does the sled speed up, slow down, or keep the same speed?

The Attempt at a Solution

I would think that when she falls off the sled, the speed of the sled should increase because m₂ got smaller, so to conserve momentum, v₂ should get larger
m₁v₁ = m₂v₂


however, the answer is that the sled keeps the same speed... why?

Remember she fell sideways off the sled, taking her momentum with her.

 

[gkangelexa]

Remember she fell sideways off the sled, taking her momentum with her.

Would she not have "taken her momentum with her" if she had fallen off the back instead of sideways?

 

[PeterO]

Would she not have "taken her momentum with her" if she had fallen off the back instead of sideways?

Yes she would. BUT if she took her life in her hands, stood up, then kicked forward on the sled so that she "left the sled" with zero momentum, the sled would have continued with all the momentum - back to its original speed.

That "kicking off" is the way people commonly dismount from a skate board, on which they are already standing.

Peter

By the way, you were only asked what would happen if she fell out sideways!