Where does the energy go if I raise and lower a block?

[nhmllr]

Okay, let's say I'm holding a wooden block. I then raise it above my head, then lower it to it's original position.

Neither the kinetic or gravitational potential energy of the block has changed, so I have done no work on the block. However, I expended chemical energy to perform this action. Where does that energy go? Into the block?

For example, if I shook a bottle of water up and down really fast then brought it back to its original position, the water will still be moving around, so wouldn't I have done work on it because I've put kinetic energy into the water in the bottle? Would I have done less work if I raised it and lowered it slowly, causing little movement in the water?

Or is the water example fundamentally different from the block example?

 

[HallsofIvy]

Basically, it is inefficiencies in your muscle that account for your not getting the energy "back". It goes into increased heat in your body, a little increased heat in the air, because of air resistance, and, if you let the block hit the ground "hard", increased heat in the ground and block.

Generally, the answer to "where does the energy go" is "into heat".

 

[drphysica]

Work done = Force x distance what are you talking about that no work is done?
the work is done for everytime you lift the brick.

 

[nhmllr]

Basically, it is inefficiencies in your muscle that account for your not getting the energy "back". It goes into increased heat in your body, a little increased heat in the air, because of air resistance, and, if you let the block hit the ground "hard", increased heat in the ground and block.

Generally, the answer to "where does the energy go" is "into heat".

Okay, let's say my arm was perfectly efficient. Or let's say that the block is a magnet that we suspend on top of a perfectly efficient electro magnet that strengthens and weakens in it's field, causing the block to move up and down. Basically what I'm saying is, if there are no inefficiencies, where does the energy go?

 

[thegreenlaser]

If your arm is perfectly efficient, that means that when you lift the block, you transfer potential energy to it, and when you lower the block it must transfer that energy back to you somehow. The energy is just transferred from you to the block, and then back to you.

I think what's probably confusing you (which confuses a lot of people) is the fact that humans are inherently inefficient, and so it's hard to gain intuition for these things by thinking about the way you personally interact with objects. Humans have to expend energy to supply force, even if they're not doing any "work" in moving an object. That's why it seems intuitive that moving a block up and then back down takes energy when in fact you've done no work on the block. If your body was perfectly efficient, you wouldn't expend any energy performing that action, you would just lose some energy for a little while. Of course, in real life our bodies don't behave like this at all, and so it seems really odd.

Edit: In case it's unclear, I'm NOT trying to say that conservation of energy only works in ideal cases, I'm just saying that as soon as you ask "Well, what if my arm is perfectly efficient?" you're creating a situation which is nothing like a you lifting a block, and so imagining yourself lifting a block will most likely just confuse you.

 

[Nugatory]

Okay, let's say my arm was perfectly efficient. Or let's say that the block is a magnet that we suspend on top of a perfectly efficient electro magnet that strengthens and weakens in it's field, causing the block to move up and down. Basically what I'm saying is, if there are no inefficiencies, where does the energy go?

If there were no inefficiencies, the the work you did lifting the block would be converted into an increase in gravitational potential energy. Then when the block came back down that potential energy would be converted into kinetic energy as the block accelerated under the influence of gravity, and it would be moving fairly quickly. Whatever is slowing the block so that it ends up at rest when gets back to ground level is dissipating that energy as heat.

Now, you could, with mythical perfectly efficient devices, arrange to rest the block on a mythical perfectly efficient spring. Then you could push the block down on the spring to compress it (doing work on and adding potential energy to the spring), and release the spring. The mythical perfectly efficient spring would accelerate the block upwards, converting all of the potential energy into kinetic energy of the moving block. The block would move upwards, slowing down and exchanging kinetic energy for gravitational potential energy, until its speed reached zero and it started to fall back down again, turning the potential energy back into kinetic energy... and in this mythical perfectly efficient world we wouldn't lose any energy to friction with the air, so the block would come down and compress the myhtical perfectly efficient spring with all the energy that we started with, and the cycle would repeat itself.

In this mythical perfectly efficient world you could keep the block moving up and down without ever losing any energy; no input beyond your initial shove would be needed. It's basically the same problem as an ideal pendulum in a mythical perfect vacuum hanging from a mythical perfectly frictionless hinge - give it a push and it will go forever in this mythical perfectly efficient world.

Did I mention that we're talking about a mythical world here?

 

[russ_watters]

Okay, let's say my arm was perfectly efficient. Or let's say that the block is a magnet that we suspend on top of a perfectly efficient electro magnet that strengthens and weakens in it's field, causing the block to move up and down. Basically what I'm saying is, if there are no inefficiencies, where does the energy go?

If you replace your arm with a spring, the energy just keeps bouncing back and forth between kinetic and two different kinds of potential energy.

But your arm, like a hydraulic lift, is not capable of absorbing and storing mechanical energy. So the act of lowering the object is always just a loss. Even if 100% efficient, it would only be a 1-way lifting device.