Energy needed to raise an object to a certain altitude

[Warp]

My thinking is that because of the law of conservation of energy, the amount of energy needed to raise an object to a certain altitude has to be at least as much as the amount of energy released by the object if it were to be dropped from that altitude and hit the ground (and all that released energy gathered somehow). I'm thinking that it has to be at least that much because if you needed to spend less energy raising the object than it releases when it falls, you could use part of the released energy to raise it again, and get the remaining energy from nothing (which is impossible).

But then I got thinking: If you used a helium balloon to raise said object, what exactly is expending the energy to raise the object? Where is that energy coming from? What is it away from? What loses that amount of energy in order to have the object raised to that altitude, transferring it that much potential energy?

 

[A.T.]

What loses that amount of energy in order to have the object raised to that altitude, transferring it that much potential energy?

The air in the atmosphere.

 

[Warp]

The air in the atmosphere.

So... how does this manifest, exactly? Does the air get colder or something? What's the mechanism of energy transferral?

 

[Baluncore]

What's the mechanism of energy transferral?

When the balloon goes up, a more dense part of the atmosphere comes down to fill the void left by the balloon. That falling atmosphere provides PE to the object being raised.

 

[Warp]

Do I understand correctly that the air loses some potential energy and the arising balloon+object gains it?

But now, if the object (let's say it's a metallic ball) is let loose from the balloon, it will fall down and release energy when it impacts the ground. In the atmosphere, however, not much has changed. Where did that impact energy come from?

Is this, like, some kind of rather convoluted way of transferring the energy used to fill up the balloon with helium to the object, or something along those lines?

 

[jbriggs444]

Do I understand correctly that the air loses some potential energy and the arising balloon+object gains it?

Yes. The bulk of the atmosphere is lowered as it lifts the balloon + object + helium.

But now, if the object (let's say it's a metallic ball) is let loose from the balloon, it will fall down and release energy when it impacts the ground. In the atmosphere, however, not much has changed. Where did that impact energy come from?

The change in potential energy of the atmospher is greater than the change in potential energy of the ball alone.

Realize that it takes a pretty large balloon to lift a pretty heavy ball. The weight of the displaced air is equal to the weight of the helium + balloon + metallic ball that was lifted by atmospheric buoyancy.

Think about continuing the scenario. If you try to pull the inflated balloon back down, you will have to supply energy. That energy can be thought of as lifting the atmosphere back up to make room for the inflated balloon.

 

[russ_watters]

But now, if the object (let's say it's a metallic ball) is let loose from the balloon, it will fall down and release energy when it impacts the ground. In the atmosphere, however, not much has changed. Where did that impact energy come from?

From the work done by the atmosphere to lift it, as described above.

Is this, like, some kind of rather convoluted way of transferring the energy used to fill up the balloon with helium to the object, or something along those lines?

That would depend on where the helium came from in the first place. Google tells me much of it is separated from natural gas, which comes out of the ground pressurized. There's a lot of potential energy in the pressure and buoyancy, but I don't know if it is more than the energy needed to separate it from the natural gas or who's ledger sheet that energy is recorded on (the helium or natural gas's).

 

[A.T.]

But now, if the object (let's say it's a metallic ball) is let loose from the balloon, it will fall down and release energy when it impacts the ground. In the atmosphere, however, not much has changed. Where did that impact energy come from?

Are you familiar with Archimedes' principle?
https://en.wikipedia.org/wiki/Archimedes'_principle

Whatever was lifted up by buoyancy weighted less than the air that went down to fill its place. So the atmosphere always looses more potential energy than the floating up objects. That is where their energy comes from.

Note that if you use balloons of the same volume with and without the metal ball:
- The balloon without the ball will raise faster and dissipate more energy through drag.
- The balloon with the ball will instead put that energy into the potential energy of the dumped ball, which is dissipated on ground impact.

So there is a difference in the atmosphere between the two cases.