# Does the gas inside a balloon affect the buoyancy?

PhyIsOhSoHard
There's something that I don't understand about the buoyancy formula.

Is the buoyancy defined by the density of the gas inside a balloon multiplied by the volume of the balloon and multiplied by the gravitational acceleration?

Or

Is the buoyancy defined by the density of the air surrounding the balloon multiplied by the volume of the balloon and multiplied by the gravitational acceleration?

When calculating the buoyancy of a balloon, do you use the density of the gas inside the balloon or the density of the air surrounding it?

ModusPwnd
You consider the density of the air surrounding the balloon to find its buyout force.

The density of the air in the balloon will contribute to the weight of the balloon. Summing these together will give you the acceleration of the balloon via newton's second law.

Staff Emeritus
The air buoys you upwards a bit, and even a block of uranium (which is much more dense than you are). The buoyant force exerted by air on an object is equal to the weight of the quantity of air displaced by volume of the object.

PhyIsOhSoHard
You consider the density of the air surrounding the balloon to find its buyout force.

The density of the air in the balloon will contribute to the weight of the balloon. Summing these together will give you the acceleration of the balloon via newton's second law.

Does this mean that the density of the air or gas inside the balloon has no direct link to the buyout force of the balloon?

PhyIsOhSoHard
The air buoys you upwards a bit, and even a block of uranium (which is much more dense than you are). The buoyant force exerted by air on an object is equal to the weight of the quantity of air displaced by volume of the object.

So whether you fill up a balloon with air or you fill it up with helium or an entirely 3rd gas, the buyout force is the same in every case considering the balloon is surrounded by the same air in all of the cases?

ModusPwnd
Does this mean that the density of the air or gas inside the balloon has no direct link to the buyout force of the balloon?

Yes. It has an affect on the balloon's acceleration and hence its movement. But it does not affect it's buoyant force. That is a function of the displaced gas/liquid and gravity alone.

So whether you fill up a balloon with air or you fill it up with helium or an entirely 3rd gas, the buyout force is the same in every case considering the balloon is surrounded by the same air in all of the cases?

The buoyant force is a function of the displaced gas/liquid. How much is displaced is a function of the balloon size which is a function of what it is filled with (unless its rigid). So you might say there is an implication for the buoyant force, an implicit implication rather than an explicit implication.

Homework Helper
So whether you fill up a balloon with air or you fill it up with helium or an entirely 3rd gas, the buyout force is the same in every case considering the balloon is surrounded by the same air in all of the cases?
Yes, buoyant force would be the same.

Whether that buoyant force is greater than the weight of the balloon would depend on the density of the gas inside of the balloon.

PhyIsOhSoHard
I see!
I learned something new today. Thank you everybody, that was very interesting. :)