A 1 gallon helium balloon is tied down by a string. Find the tension.
(The density of air is 1.29 kg/m3, the density of Helium is 0.179 kg/m3,
and 1 cubic meter is equal to 264 gallons.)

Question

A 1 gallon helium balloon is tied down by a string. Find the tension.
(The density of air is 1.29 kg/m3, the density of Helium is 0.179 kg/m3,
and 1 cubic meter is equal to 264 gallons.)

anonymous · Answer

A helium balloon in air is like an air bubble in water. That's right, we are dealing with buoyant force here, by the air around the helium balloon.

One gallon of air is displaced, hence we have the force equal to weight of that much air on the balloon upwards. Gravity pulls the helium balloon down. It'll be weaker than the buoyant force though. To keep that balloon from flying off upwards due to the net upward force, you have the string holding it in place. It holds it in place by balancing the remaining force of gravity. That difference is the tension in the string.