I What Explains the Paradox of Mechanical Energy Conservation?

[Chenkel]

TL;DR Summary

I give a thought experiment of a rollercoaster and a ball in the hand.

Hello everyone! I've been studying work and energy, and one problem I have is understanding conservation of mechanical energy. If on a rollercoaster you have two points A and B you expect the mechanical energy at A to be equal to the mechanical energy at point B, makes sense to me; but I started wondering, what if I have a ball in my hand and move it from above my head to below my head, the potential energy changes at the two points, but the kinetic energy is 0 at both points, it makes me wonder what the non conservative forces are and why they are considered non conservative, how can I explain this lack of conservation of mechanical energy? Let me know what you guys think, thank you!

 

[kuruman]

What is your system? Choose any number from (a) rollercoaster; (b) ball; (c) you; (d) Earth.

Whatever you choose, your muscles exert a non-conservative force on the ball.

 

[berkeman]

Summary: I give a thought experiment of a rollercoaster and a ball in the hand.

Hello everyone! I've been studying work and energy, and one problem I have is understanding conservation of mechanical energy. If on a rollercoaster you have two points A and B you expect the mechanical energy at A to be equal to the mechanical energy at point B, makes sense to me; but I started wondering, what if I have a ball in my hand and move it from above my head to below my head, the potential energy changes at the two points, but the kinetic energy is 0 at both points, it makes me wonder what the non conservative forces are and why they are considered non conservative, how can I explain this lack of conservation of mechanical energy? Let me know what you guys think, thank you!

Wowie.

What is "mechanical energy"? Please post a link and give an exact mathematical definition. Thank you.

Is the roller coaster car moving? If so, why is the ball's KE zero?

 

[Chenkel]

I just found this on Google

"Non-conservative forces are dissipative forces such as friction or air resistance. These forces take energy away from the system as the system progresses, energy that you can't get back. These forces are path dependent; therefore it matters where the object starts and stops."

I suppose because the hand is slowing down the ball, the energy of the hand takes the energy away from the ball, but it's a little unclear to me how this is happening because two objects interacting does not necessarily mean transfer of energy from one system to another.

 

[Chenkel]

Wowie.

What is "mechanical energy"? Please post a link and give an exact mathematical definition. Thank you.

Is the roller coaster car moving? If so, why is the ball's KE zero?

Apologies if I wasn't clear enough, the ball throwing is happening outside the rollercoaster ride, I'm just making a comparison between the rollercoaster and the ball, an example where kinetic energy is conserved vs an example where it's not.

The definition of mechanical energy from Wikipedia:

"In physical sciences, mechanical energy is the sum of potential energy and kinetic energy. The principle of conservation of mechanical energy states that if an isolated system is subject only to conservative forces, then the mechanical energy is constant"

 

[Nugatory]

Presumably by "mechanical energy" you mean the sum of the kinetic energy KE and potential energy PE?

As @kuruman points out, the muscles are exerting a non-conservative force so that mechanical energy is not conserved, and this makes the problem a bit harder to think through. Nonetheless, the total energy (which is the sum of KE, PE, the chemical potential energy in your muscles, and the heat dissipated in your muscles as they move) will be conserved.

 

[Chenkel]

Presumably by "mechanical energy" you mean the sum of the kinetic energy KE and potential energy PE?

As @kuruman points out, the muscles are exerting a non-conservative force so that mechanical energy is not conserved, and this makes the problem a bit harder to think through. Nonetheless, the total energy (which is the sum of KE, PE, the chemical potential energy in your muscles, and the heat dissipated in your muscles as they move) will be conserved.

So as my muscles bring something to a stop I imagine they heat up, can that heat be transferred back to the ball in the form of KE? How do muscles have potential energy relative to the ball? The muscles use calories, and the ball never gives energy back to the muscle so I'm having trouble invisionioning a system where the energy is conserved.

 

[russ_watters]

So as my muscles bring something to a stop I imagine they heat up,

Yes.

can that heat be transferred back to the ball in the form of KE?

No.

How do muscles have potential energy relative to the ball?

Huh? They...don't. I don't know what your thought process is there.

The muscles use calories, and the ball never gives energy back to the muscle so I'm having trouble invisionioning a system where the energy is conserved.

It's a good bet that any unaccounted for energy ends up as heat.

 

[Dale]

two objects interacting does not necessarily mean transfer of energy from one system to another

This is wise to notice. So, two objects interact (meaning they exert forces on each other), what determines if energy is being transferred?

The rate of energy transfer is known as power and is given by $P=\vec F \cdot \vec v$. So energy is transferred whenever the force is in the direction of the velocity.

In the case of lowering a ball in your hand, the velocity is vertical and the force is vertical, so mechanical energy is indeed transferred in this scenario.

FYI, my recommendation is to avoid trying to analyze the human body in introductory physics courses. It is a very messy machine and more likely to confuse than illuminate. Always try to replace it with a simple machine. In your case, try thinking about lowering the ball using a spring.

 

[Ibix]

So as my muscles bring something to a stop I imagine they heat up, can that heat be transferred back to the ball in the form of KE?

No, but regenerative braking in electric cars does something of the sort. Instead of dissipating kinetic energy as heat they use it to turn a generator and charge the battery.