As I mentioned before in the thread, if the balloon is in equilibrium with the atmospheric pressure at 4 feet, it will try to sink back down to a 4 foot altitude, thus hitting the upstairs floor.
Of course, in real life it’s more complicated, and it is likely that the balloon will hover at 4 feet or so, since the hot air near the top of the room will be less dense than cool air lower down in the room. I don’t believe that the elasticity of the balloon is going to have any measurable effect, nor will the actually negligible air pressure differences between 4’ and 14’ make a difference when compared to the effect of air temperature and the associated density change of said air.
Nor will a string have much effect. If you placed the helium balloon in an atmosphere of dense gas, it would float higher, string or no string, than if it were in a vacuum, in which it would fall to the floor like a stone.
Upstairs or down, a balloon will float at the height above the floor where its density, envelope plus contents, exactly matches the density of the air around it.
Since cool air is more dense than warm.the exact position at which the balloon floats depends on the temperature profile of the room. If your balloon or blimp is neutrally bouyant in 73.5 degree air, and the temperature is 73.5 degrees 4 feet above the floor downstairs, and 8 feet above the floor upstairs, then the balloon, will float 4 feet above the downstairs floor, or 8 feet above the upstairs floor.
However I did buy a radio-controlled helium balloon with a motorised fan (like this).
It would generally hover about 6 feet up (most of the rooms in my school are the same temperature if that helps).
I flew it in my School Library. Pupils would gasp in amazement.
I flew it in my School Sports Hall, which has a ceiling about 20 feet high. Unfortunately after I flew it to the ceiling, the battery ran out and it was stuck. To retrieve it, I needed a 15 foot long thin wooden pole, which bent alarmingly (but perhaps that’s another thread…)
Well, no, not exactly. I was assuming the balloon posited by the OP is neutrally buoyant (or really close to it)–otherwise, it’ll either rise or sink. Given still air, it will float where you put it.
No, Q.E.D. has it quite right, and the density explanation is misleading in its own way. When a balloon goes up or down, there must be a force doing this. You can’t simply say it’s because of the density difference – there must be a force causing the acceleration. The origin of that force is the variatio in pressure with height due to the effect of gravity – the air pressure is slighlty less on the top of the balloon than on the bottom, so the forces are unbalanced, and the balloon goes up. If there was no gravity but still a density difference (as on, say, the Space Station), the balloon doesn’t go anywhere.
As for the question about the string – that’s a little complicated. If the string is on the ground and exerting frictional force, it might help keep the balloon down. But if the string is not on the ground, it’s just ballast, like the part of the ballon past where it’s tied off. It’s not helping keep the balloon up (by helping enclose the gas), so it’s just dead weight adding to the overall set of forces acting on the alloon.
For a balloon that is balanced at a particular height in still air, the downward forces due to gravity on its weight (and that of any attached dead weight) exactly balances the upward forces due to the lower density of the gas (ating through the pressure differential). To give ivn his due, the averaged density of the balloon and all it contains ought to equal that of the air at this point. It seems to me that the ballon, if it really is floating 4 feet off the floor on the ground floor, ought to go to the floor if you take it upstairs.
If you don’t believe this, try the following gedanken experiment – imagine that you have the balloon on the first floor and you magically eliminate the ceiling, so the lower floor and the upper are connected. Won’t the balloon stay where it is? Now imagine the balloon is on the upper floor and you remove the floor. Won’t the baloon fall until it’s 4 feet from the lower floor?
In real life, all sorts of things can bollix this up, if you actually try it. Differences in temperature might change the ballon’s bouyancy. Air currents might push it around. You might accidentally add or take way something, changing its weight. Heck, static electricity mitght even have an effect.
To clarify, the string can (but doesn’t always) do more than act as dead weight or a frictional stop on the balloon. It can act as a variable ballast on the balloon.
For example, say the balloon can lift 50g, which happens to be the weight of a piece of string 50cm long. If there is a meter long string attached to the balloon, 50cm of the string will rest on the floor, and the balloon will then float 50cm high. If you added another 10g of lift to the balloon, the balloon would then float at 60cm (40cm rests on the floor), etc. But imagine that you moved the balloon to a table. It will float 50cm above the table, because the table is supporting the excess 50g of string above the floor.
CalMeacham, I think you are dead on. I didn’t think the OP featured a dragging string, and your thought experiment is what I had in mind. And you are right about what causes a balloon to rise (Q.E.D.'s post), but I didn’t think that it gave a clear enough picture as to why a balloon would hover at a specific altitude.
For a practical demonstration, if you tie a weight to the string on a balloon, and hold the weight in your hand, you can alter the balloon’s height just by lifting or lowering the weight. A length of string heavier than the lift generated by the balloon does the same.
