Question

If the mass of the material the balloon is made of is 0.01 kg, how much mass could you attach to the He balloon and still have it float (in kg)? (The density of He gas at the pressure and temperature in the room is 0.14 kg/m^3).

Answer 1

Given: mass of balloon , m_b = 0.01 kg

density of helium, ρ_He = 0.14 kg/m³

density of air, ρ_air = 1.225 kg/m³

Assumption : volume of material of balloon is negligible

Let the volume of expanded balloon be V

For balloon to float in air, upward force should be equal to downward force on it

Upward force = buoyant force

Downward force = Weight of balloon + weight of helium

Weight of balloon + weight of helium = buoyant force due to air

m_bg + ρ_HeVg = ρ_airVg

V = m_b/(ρ_air - ρ_He)

V = 0.01 / (1.225 -0.14)

V = 9.2166 × 10^-3 m³

Mass of helium to be attached, M_He = ρ_He × V

M_He = 0.14 × 9.2166 × 10^-3

M_He = 1.29 × 10^-3 kg = 1.29 g

So, maximum of 1.29 gram of Helium can be attached.