### Where does the energy go?

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Suppose you expend energy to lift an object up and put it back down. The initial and final positions are the same.

Where does the energy go?
Is this a Force vs. Work kind of question?
Don't take my every word for it, say you had a ball being held in the air. You have gravitational potential energy - energy due to position and influence of the acceleration of gravity. When you drop it, upon impact of a surface compression results in heat energy and possible elastic potential energy. Some of the energy gets converted as vibrational pulses of sound waves. Energy is not just due to displacement.
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hmm well the in depth maths of this gets quite tricky. Anyway, let's lift a box.

When you lift the box, you increase the gravitational potential energy of the box. You can see this as actually increasing the total energy of the system of the box. You are actually increasing its mass (E - m c^2).

Let's say you now drop the box (that's just a very fast way of putting it down). The gravitational potential energy of the box is converted to kinetic energy. The box will accelerate until it hits the floor. Once it hits the floor, this kinetic energy will be dissipated. Some of it will turn to kinetic energy in the floor, some will turn into kinetic energy in the box, some will turn into sound, plus a few other things that are not very interesting. If a large amount of energy was involved (or it was a weak box or floor) you might see some of the energy used to break bonds between atoms in the molecules of the box or floor and the shape of the box, floor or both could be changed.

End result? (ignoring wastage in muscles, due to air resistance and other things that aren't interesting to us)

The energy from your cells was put into the box when you lifted it. That extra energy you put into the box was released, mostly as kinetic energy, when it hit the floor.

Disclaimer: I'm not a physics student or professor. This is just what I understand from studying physics for fun.
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If you continually lift weights up and down, you use up energy - where is that energy going?
If you just sit there lifting a dumbbell with your arm, most of the energy is being wasted as heat. I'm sure you have felt this if you have ever do any weightlifting. You are converting energy in the cells into increasing the temperature of the environment.
 If you continually lift weights up and down, you use up energy - where is that energy going?

It's going into moving the weights? Just because the final position of the weight hasn't changed doesn't mean it wasn't moved. Moving something takes energy.

I'm not sure if I understand what this thread is about. =x
@Disch saying "it's going into moving the weights" only compounds the question. Do the weights store the energy that is going into them?

Objects have inertia - to make an object change its motion you have to apply a force, but I don't understand what happens after that. Where has the energy gone?
I think people are confused as to what are you referring to? The energy from your arm or the energy of the actual object?
What do you mean? Isn't there a transfer of energy going on here?
Yes, that is the rule of the conservation of energy. I meant are you attempting to ask where does the mechanical energy induced/converted by the movement of your muscles go?
 Do the weights store the energy that is going into them?

Yes.
 When you lift the box, you increase the gravitational potential energy of the box. You can see this as actually increasing the total energy of the system of the box. You are actually increasing its mass (E - m c^2).

 It's going into moving the weights? Just because the final position of the weight hasn't changed doesn't mean it wasn't moved. Moving something takes energy.

See above answer about the box. Edit: When you're lifting weights, most of the energy is lost as heat, but if we ignore that...

 Objects have inertia - to make an object change its motion you have to apply a force, but I don't understand what happens after that. Where has the energy gone?

If you move an object, you are accelerating it. As you accelerate it, you increase its mass (or energy. Energy = mass * c ^ 2). Whenever you apply force to something, you are always increasing its energy/mass. That is where the energy has gone.
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Your arms transfer kinetic energy to the dumbbells to raise them up, and that energy is "stored" as gravitational potential energy. That energy is then used when you let them back down (letting gravity displace them). The excess energy can be explained as having gone into overcoming air friction and the heat that gets generated by your arms.
@Mats:

Apparently I need to take a physics class because nothing you said makes sense to me. I wouldn't think the mass of an object increases simply because force is being applied to it. I thought mass was a property of matter, not of energy.
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Doesn't that fall under special relativity ? At the speeds we are talking about you will see almost no change in mass. It's closer to the speed of light that mass begins to increase (which is why it's theoretically impossible to surpass the speed of light).
Disch wrote:
I thought mass was a property of matter, not of energy

Matter and energy are equivalent, hence the matter-energy equivalence equation E = mc2.

xerzi wrote:
almost no change

Almost none =/= none. At such low speeds we are talking about relatively small transfers of energy, so it follows that it would correspond to very small changes in mass.
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closed account (o1vk4iN6)
 Almost none =/= none.

Hence why I didn't say none ;). It's so small it is simply ignored in most calculations is what i meant (course it all depends what you are doing, in this instance moving an object with your arm suites fine).
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@Mats thanks, it was the idea of energy transfer being associated with change in acceleration that I was missing.
Energy goes into pushing air away?
Or did you mean "how does my force lift a box" ?
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@EssGeEich: neither, apparently mats is the only person who understood me.
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