Is Momentum of a person bouncing on a trampoline conserved?

[Physics0009]

Homework Statement

Is Momentum of a person bouncing on a trampoline conserved?

Homework Equations

p=mv
conservation of momentum equation

The Attempt at a Solution

Please explain in detail (if possible). Thanks!

 

[collinsmark]

What do you think? :tongue: (Hint: Before answering that, think: Newton's third law of motion. Does the momentum of the Earth fit into the answer?)

 

[Physics0009]

So yes, the trampoline and the person apply equal and opposite forces on each other, leading to conserved momentum? If momentum is conserved, ultimately, how come the person stops bouncing?

 

[collinsmark]

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.

 

[rdl]

I can say that the momentum of a person bouncing on a trampoline is not conserved. This is because the conservation of momentum states that the total momentum of a system remains constant unless an external force acts on it. In this case, the person is constantly exerting a force on the trampoline as they bounce up and down, and the trampoline is also exerting a force back on the person. This means that the total momentum of the system (person + trampoline) is changing as the person bounces.

Furthermore, as the person bounces higher and higher, their velocity increases, which means their momentum also increases. This increase in momentum is not being balanced by an equal decrease in momentum elsewhere in the system, so the total momentum is not conserved.

Additionally, when the person reaches the top of their bounce and starts to fall back down, their momentum is changing direction, which also goes against the principle of conservation of momentum.

However, it is important to note that while the total momentum of the system is not conserved, the momentum of each individual component (person and trampoline) is conserved. This means that the person's momentum may be changing, but the trampoline's momentum is also changing in the opposite direction to balance it out.

In conclusion, the momentum of a person bouncing on a trampoline is not conserved due to the external forces acting on the system.