Helium has a density of 0.1786 kg/m3, and air has a density of 1.275 kg/m3. If a balloon is filled with 0.1 m3 of helium, how heavy can the balloon itself be before it will no longer float?

Question

Helium has a density of 0.1786 kg/m³, and air has a density of 1.275 kg/m³. If a balloon is filled with 0.1 m³ of helium, how heavy can the balloon itself be before it will no longer float?

1. What is the mass of helium in the balloon?
2. What is the maximum mass of the balloon?

Answer 1

The volume of the balloon material itself is insignificant, so we will say that the volume of the balloon and the helium inside it is 0.1 m³. Let b be the mass of the balloon. Then the mass of the balloon inflated with 0.1 m³ of helium is b + 0.01786 kg. The critical value of b is the mass that brings this sum up to the mass of the same volume of air, which is 0.1275 kg.

So, b = 0.1275 kg - 0.0179 kg = 0.1096 kg