Physics0009 said:
So yes, the trampoline and the person apply equal and opposite forces on each other, leading to conserved momentum?
Essentially, yes (but you haven't included one other part of the whole system). What is the trampoline itself attached to?
When a person pushes against the trampoline (or should I say, when trampoline/Earth pushes against the person), we know what happens to the person: the person bounces
up. And at the same time, what happens to the trampoline/Earth? Does it also bounce? And if so, in what direction?
If momentum is conserved, ultimately, how come the person stops bouncing?
Conservation of momentum is different than conservation of kinetic/potential energy. There are frictional energy losses involved, and conservation of kinetic/potoential energy does not necessarily apply in that case. (Overall conservation of energy applies, but kinetic and/or potential energy might be converted to some other types of energy such as heat.)
Back to conservation of momentum. Allow me to say that in a general sense: For a closed system, where no
external forces or torques are present (
internal forces and torques are allowed), momentum is
always conserved. This is true whether friction is involved or not. I leave it to you to show how this applies to the trampoline situation.
(Hint: Before answering that, think: Newton's third law of motion. Does the momentum of the Earth fit into the answer?)