Conservation of Energy in Trampoline Bounce

[ManfredArcane]

Homework Statement

A person with a mass of 50kg falls onto a trampoline with a downward speed of 4.89 m/s. Due to the trampoline, the person experiences a net upward force of 887 N for a time of 0.578 s.

The person leaves the trampoline with a speed of ___ in the upward direction.

Relevant Equations

P0+J=Pf
KE0+PE0+Wnc=KEf+PEf

I was able to calculate the correct answer (given by a solution sheet), V=5.364 m/s, using the momentum impulse equation, P0+J=Pf. If this value is correct, however, I don't understand how energy is being conserved. The speed increases after the person bounces off the trampoline while the mass remains constant. Thus there is a net increase in kinetic energy. The only answer that I can think of is that the problem statement treated the trampoline as applying a force to the person that was not commensurate with the action of a spring, in other words, as doing non-conservative work. I just want to make sure I am not missing something here conceptually. Thanks, and sorry if I made any mistakes with this post.

 

[Orodruin]

the person experiences a net upward force of 887 N*m

That is not a force. The units are wrong.

 

[ManfredArcane]

My mistake, the unit given in the problem was Newtons.

 

[Orodruin]

Presumably the person also expended energy in jumping off the trampoline. Like people do when they, you know, jump on trampolines to get higher and higher.

 

[erobz]

Homework Statement:: A person with a mass of 50kg falls onto a trampoline with a downward speed of 4.89 m/s. Due to the trampoline, the person experiences a net upward force of 887 N for a time of 0.578 s.

The person leaves the trampoline with a speed of ___ in the upward direction.
Relevant Equations:: P0+J=Pf
KE0+PE0+Wnc=KEf+PEf

I was able to calculate the correct answer (given by a solution sheet), V=5.364 m/s, using the momentum impulse equation, P0+J=Pf. If this value is correct, however, I don't understand how energy is being conserved. The speed increases after the person bounces off the trampoline while the mass remains constant. Thus there is a net increase in kinetic energy. The only answer that I can think of is that the problem statement treated the trampoline as applying a force to the person that was not commensurate with the action of a spring, in other words, as doing non-conservative work. I just want to make sure I am not missing something here conceptually. Thanks, and sorry if I made any mistakes with this post.

Firstly, the problem states the person falls on a trampoline. Secondly, Due to the trampoline, the person experiences a net upward force of 887 N for a time of 0.578 s.

Given this problem statement, you are completely justified in your concern. This shows that you are a critical reader, and thinking more deeply and accurately than you were given credit for ( don't let the snide remark get under your skin).

Good catch!

 

[Orodruin]

Firstly, the problem states the person falls on a trampoline.

Which is typically what happens when you are in the air above a trampoline.

Due to the trampoline, the person experiences a net upward force of 887 N for a time of 0.578 s.

Which is also perfectly valid for someone jumping on a trampoline. Even when jumping, the force providing the impulse is that on the person due to the trampoline. If you jump off the ground, the force that provides the impulse on you as a system is that from the ground acting on you, even if that force is doing no work.

Don't let the snide remarks get under your skin.

There was nothing snide intended about the remark. Your interpretation in making it so and making a snide comment of your own is however noted.

It is perfectly valid to ask questions to get clarification when something does not match up in your head. It is another to make snide remarks about perfectly valid resolutions.

 

[erobz]

The energy input is not due to the trampoline.

 

[Orodruin]

The energy input is not due to the trampoline.

That is irrelevant. The force is and it is the force that is given and supplies the impulse.

 

[erobz]

Like people do when they, you know, jump on trampolines to get higher and higher.

Are seriously trying to claim that your remark here is not belittling?

 

[erobz]

That is irrelevant. The force is and it is the force that is given and supplies the impulse.

The OP was asking how energy was not conserved, and whether or not he was thinking about it correctly. And they were perfectly correct.

 

[Orodruin]

Are seriously trying to claim that your remark here is not belittling?

Yes. But you may read into it what you will. It is the internet and people will read things differently than they are intended.

You are however changing the subject.

The OP was asking how energy was not conserved, and whether or not he was thinking about it correctly. And they were perfectly correct.

The OP is perfectly entitled and correct to ask for clarification because indeed kinetic energy is higher after contact. It is however the case that the situation I described is well within the constraints of the problem formulation and also describes a situation where the kinetic energy after trampoline contact would indeed be increased due to the release of chemical energy in the person’s legs. Making snide remarks about however I formulated myself does not change this.

 

[PeroK]

The OP was asking how energy was not conserved, and whether or not he was thinking about it correctly. And they were perfectly correct.

How does anyone ever emerge from an armchair if their kinetic energy is conserved?

 

[erobz]

How does anyone ever emerge from an armchair if their kinetic energy is conserved?

In the context of an idealization of a mass falling on to a spring (which the OP's problem obviously is), an increase in kinetic energy is absolutely suspicious.

 

[Orodruin]

How does anyone ever emerge from an armchair if their kinetic energy is conserved?

Seriously though, this issue is something many people wonder about when starting physics: How you can jump off the ground when the force from the ground on you does no work. The resolution being that the energy is added elsewhere (by expending chemical energy stored in the muscles), but the impulse comes from the ground. Looking at the full flow of energy and momentum is quite beyond introductory mechanics though.

In the context of an idealization of a mass falling on to a spring (which the OP's problem obviously is), an increase in kinetic energy is absolutely suspicious.

(My emphasis) I disagree. This is your interpretation but there is nothing in the problem as stated that actually tells you this. You are given a falling speed before the person hits the trampoline and a force. The typical idealized elastic mass on spring problem would have been unlikely to give you the force (although it might ask you to compute the force at some point of the peocess).

 

[PeroK]

In the context of an idealization of a mass falling on to a spring (which the OP's problem obviously is), an increase in kinetic energy is absolutely suspicious.

An inert mass cannot get up out of an armchair, but a person can. That's the point, surely?

 

[Orodruin]

Just as an aside, while I do believe it is the clear intent of the problem author to highlight a jump with resulting higher speed, he/she should be more careful with the use of significant digits … considering the mass of the person has one or possibly two significant digits at best, having an answer and other input with four seems excessive.

 

[kuruman]

I see this problem as an inelastic explosion between trampoline and the person. The extra energy of the explosion comes from biochemical energy stored in the person's muscles. I see nothing wrong modeling it like this.

 

[erobz]

An inert mass cannot get up out of an armchair, but a person can. That's the point, surely?

No...none of this group attack is actually the point. The point was to confirm to the OP that his interpretation of a person as an idealized mass falling on an idealized spring somehow gaining kinetic energy was indeed suspicious without being cheeky about it. Are you seriously teachers. I pity your students...

 

[PeroK]

Are you seriously teachers. I pity your students...

I was a PE teacher but none of my students could do anything because of what they learned from a dodgy physics teacher. "We can't run or jump, sir" they used to say "because of energy conservation!"

 

[erobz]

I was a PE teacher but none of my students could do anything because of what they learned from a dodgy physics teacher. "We can't run or jump, sir" they used to say "because of energy conservation!"

See...Understanding what to expect of an assumed model is an important developmental objective.

 

[berkeman]

Thread is closed. I think we all saw the problem with the initial statement of the problem, and tried to help the OP understand what may have been going on instead.

@erobz -- check your PMs.