Why Don't Air-Filled Balloons Float?
Empty balloons bought at the store, upon being blown up, don't float. In fact, if one holds a blown-up balloon in the air, it will sink.
Sink or Float
Opening the back of a toilet, one might find a metal ball floating on water. Take another metal ball such as that one and flatten it, fold it in half and flatten it again, and so on until the metal is as small as it can get, and put that in the water; it will sink. Why?
Density
It's a matter not of weight alone, but of density. The equation for density is,
Density = Weight / Volume, or D = W/V.
The flattened metal weighs about the same as the metal ball. However, the volume is much smaller after pounding.
Calculations Example
Say the metal piece is now 1/2" x 1/2" x 1/2". Before that, it was a sphere 4" wide. The volume of the flattened piece of metal is 0.1250 cubic inches. The volume of the sphere is 4/3 π r³, or 33.50 cubic inches.
Now say the metal weighs a twentieth of a pound. Then the two density equations become,
0.0500 / 0.1250 = 0.4000 lbs. per cubic inch for the piece of metal.
0.0500 / 33.50 = 0.0015 lbs. per cubic inch for the metal sphere.
Water's density is 0.0360 pounds per cubic inch.
The ball's density is less than 1/20 that of water, so it floats easily. The folded piece of metal has a density more than 10x that of water, so it sinks.
Now we've cheated in this example. We didn't figure in the weight of the air. That's very little compared with the weight of the water or metal, so it didn't matter in this case.
Back to Balloons
Switch from water to air. Change the metal to rubber. The numbers will be different. The rubber, folded up, will have a much higher density than the air-filled balloon will. The balloon should float, right? No. Why?
It's because the balloon has on its inside the same thing as what's on its outside. The weight of the air becomes important in this instance. The density of the balloon, no matter how much it is blown up, is greater than the air surrounding it.
A More Complete Equation
A more complete equation reads,
D = [W(skin) + W(inside)] / V(skin)
The skin could be metal, rubber or whatever we choose to hold what is inside. If we filled the balloon with concrete, it would drop fast. If we filled it with air, it would drop slowly. What if we filled it with helium? Helium is much lighter than air. It weighs only 1/7th as much as air. If we did the calculations, we would see a helium balloon would float.
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