I was writing a comprehensive answer to a question when it became protected before I could submit my answer. Could a mod please submit my answer for me? I took a lot of time to write up and research and it seems not in the spirit of the site that such research get penalized by not being able to post an answer.

Edit: And now I can't post this question because it says I can only answer a question once every 40 minutes--even though my post never went through on the question in the first place.

Here's the question: When a balloon pops and lets a brick fall, where does the energy come from?

My answer I was in the process of submitting is below:

tl; dr The energy comes from the conversion of buoyant potential energy to gravitational potential energy. That energy came from filling the balloon with enough helium to lift it and the brick off the ground.

Imagine you haven't filled up your balloon yet--you have a deflated balloon tied to a brick and sitting on the ground. Let's call the balloon brick system the airship.

The airship is at equilibrium sitting on the ground. It has no potential or kinetic energy. But then you hook up your balloon to your canister of helium and start to fill it up. As the balloon starts to fill, the volume of atmosphere displaced by the helium increases, until the weight of that displaced air becomes greater than the weight of the balloon filled with helium (this only works to lift the balloon because helium is less dense than the surrounding air). That buoyancy provides an upward force on the balloon and the airship. At this point the balloon is floating above the brick, but still lacks the force to lift the airship off the ground. The brick itself is still at equilibrium.

You keep filling up the balloon with helium, and eventually the force of buoyancy from the larger balloon provides enough upward force on the airship to overcome the force of gravity on the airship--so you stop pumping helium into the balloon by disconnecting your canister. The airship is now out of equilibrium by being on the ground and begins to rise to achieve a lower energy state.

Gravity doesn't change as your airship rises (it technically increases a little bit from the extra atmosphere beneath you, but we can ignore that). If your balloon was strong enough, you'd eventually get to a point high enough up in the atmosphere such that buoyant force exerted on the balloon decreases to the point that the airship is in equilibrium again--the buoyant force balances the gravitational force on the airship. Your airship now has a lot of gravitational potential energy! But where did it come from? It actually comes from the buoyant force which was constantly acting on the airship during the ascent. Your airship, once it was filled up enough to start rising off the ground, gained buoyant potential energy. So as your airship ascended, it was converting that buoyant potential energy to gravitational potential energy. The catch is that during the ascent, there was actually another force acting on the airship as well--the force from air resistance. So you actually lose potential energy overall by having your airship float into the sky! But that's a good thing--because if it didn't lose potential energy by ascending, it wouldn't ascend in the first place.

You might ask, where did the buoyant potential energy come from though? It came from filling the balloon with enough helium to overcome the force of gravity on the airship.

Here's a nice succinct reference I found that goes over the problem with equations: https://aapt.scitation.org/doi/pdf/10.1119/1.1466552

OP has already resolved his specific problem.

However, since a meta post is about policy making, it raises a more general issue about the future: Should a HNQ be protected after, say 3, answers? Past experience suggests a yes.

Moreover, if OP is really, really committed to answer a protected question, obtaining the required 10 reputation points on Phys.SE is not an insurmountable task.

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    I agree HNQ questions should be protected. I would even take it further: they should be protected regardless of how many answers they have. Once the post leaves the HNQ list, it may be useful to unprotect them (or not, depending on the case). – AccidentalFourierTransform Aug 10 at 15:04
  • I disagree, but I do think it makes sense to have that discussion elsewhere. Maybe I'll make a meta post about it if nobody else does first. – David Z Aug 10 at 19:09

I guess it would be technically possible, but I believe a better solution is to unprotect the question, which I've done. You can post your answer there now.

In general I don't think it's a good idea for people to be posting answers for other people. Maybe there are rare situations where it's necessary, but I think this is not one of them.

  • Thank you so much! I've posted it now. – spacetyper Aug 9 at 22:39
  • Now that the answer is posted, maybe you should restore the protected status? – gparyani Aug 9 at 23:12
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    @gparyani Eh maybe, but I don't think there's any rush. It's not like people are coming out of the woodwork to post bad answers now that the question is unprotected. – David Z Aug 10 at 1:51
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    @DavidZ That's precisely the kind of HNQ where people do come out of the woodwork and post bad answers when they're not protected. – Emilio Pisanty Aug 10 at 10:35

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