Question

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: speedu p, slow down or keep the same speed?

i knwo the answer is slow down(from my professor). Is this because since P=mv. since she drops vertically, so the mass horizontally is conserved. since new mass is added to the horizontal momentum does this mean velocity has to be lower?

Susan falls sideways off the sled but continues moving forward. When she drops off, does the sled speedu p slow down or keep the same speed?

I know the answer is same speed, but why? I don't get it. I know momentum of the system is conserved. So since it was (Mass of susan+mass of sled)*v=P now that susan mass is off and momentum needs to be conserved shouldn't velocity increase since mass decreased? i got this answer from my professor. he said that the speed is conserved even after they split. i dont get why, is it because they are both still part of the same momentum system even if they are split apart?

Answer 1

Think of Susan's interaction with the sled to be an inelastic collision. After she falls off and lands on it, the Susan - Sled system continues to move together with same velocity [hence inelastic collision]. By Conservation of momentum, the momentum of the system must be the same as before. But since the mass of the system has increased, therefore the speed of sled will be now be decreased.

If now falls off the sled, the speed of the sled will increase but only from the previously decreased speed when Susan boarded the sled. This relatively increased speed, by conservation of momentum, will be the same as the sled's initial speed. Therefore it can be said that the speed remains the same.