Buoyant force problem - can someone please explain?

[lumpyduster]

Buoyancy is something that really confuses me, so if someone could explain their thought process for solving this basic problem, I would be much obliged!

From EK 1001:

At atmospheric pressure, air is approximately seven times heavier than helium. A sealed helium balloon rises into the atmosphere. If the helium remains in thermal equilibrium with its surroundings, the balloon will rise:

A. Unit the pressure inside the balloon is equal to the pressure of the surrounding atmosphere.
B. Until the pressure inside the balloon is seven times greater than the pressure of the surrounding atmosphere.
C. Until the pressure inside the balloon is seven times less than the pressure of the surrounding atmosphere
D. The balloon will not rise if the temperature of the balloon is equal to the temperature of the surroundings.

Correct answer is B.

I think pressure inside the balloon will decrease as the balloon rises, because doesn't temperature decrease as you go up in the atmosphere? But that doesn't make sense, since the atmospheric pressure is lower at higher elevation.

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[techfan]

I think you're reading into this too much. It's not saying "How high will the balloon go?" It's asking when the balloon would stop rising. The pressure inside of the balloon has to be 7 times higher than the outside because the helium can only float when it is lighter than air and when you increase the pressure of the helium in the balloon to 7 times the mass of the helium inside of the balloon is equal to the mass of air outside.

 

[lumpyduster]

I think you're reading into this too much. It's not saying "How high will the balloon go?" It's asking when the balloon would stop rising. The pressure inside of the balloon has to be 7 times higher than the outside because the helium can only float when it is lighter than air and when you increase the pressure of the helium in the balloon to 7 times the mass of the helium inside of the balloon is equal to the mass of air outside.

I understand what you've said except the very last part. How does pressure change/affect the mass?

 

[techfan]

Well my thinking was that P=F/A and assuming that the balloon's walls are rigid (so that the volume doesn't change) the surface area (A) of the balloon is constant the only thing that is changing is Force (F). Force=ma, so I probably shouldn't have said mass and said force, or weight instead.

 

[lumpyduster]

Well my thinking was that P=F/A and assuming that the balloon's walls are rigid (so that the volume doesn't change) the surface area (A) of the balloon is constant the only thing that is changing is Force (F). Force=ma, so I probably shouldn't have said mass and said force, or weight instead.

Ah ok I think I get it. Is the force in pressure problems like this the gravitational force, though? Sorry, we didn't really cover this in physics class and I'm not quite able to teach it to myself.

 

[techfan]

Yeah, the force is the gravitational force because it's the helium particles the earth is pulling down. The easiest way to think about this is just to assume that by increasing pressure you're increasing force and therefore mass (since the acceleration of the particles probably isn't going to change very much because it's an ideal gas {I don't want to go into too much detail since that would require me actually looking back at a bunch of my thermo noted lol}).

The hint in the problem was that the air is 7 times heavier and since lighter things float on heavier things it takes the pressure to increase to 7x (need 7x as many Helium particles to fill the same volume as air particles to fill the same area). The buoyant force is nothing more than having the liquid below the object be denser than the liquid above it (for the same surface area).

No problem! It helps me learn when I have to explain things. If this answer is still confusing I'll hop on my laptop and write something more formal up with diagrams and we'll figure this buoyancy thing out.