Buoyancy & Buoyant Force Video Lessons

Concept

# Problem: The density of helium gas is 0.179 kg/m3, while the density of air at sea level is 1.29 kg/m3, A research balloon needs to carry aloft a group of scientific instruments whose total mass is 324 kg. What is the minimum radius of the spherical balloon needed to overcome gravity at sea level? The mass of the balloon material when not inflated is an additional 15.0 kg.

###### FREE Expert Solution

In this problem, we are required to determine the radius of a balloon that will give the desired lift force.

The expression for the lift force is:

$\overline{){{\mathbf{F}}}_{{\mathbit{L}}}{\mathbf{=}}{\mathbf{V}}{\mathbf{\left(}}{{\mathbf{\rho }}}_{\mathbf{a}\mathbf{i}\mathbf{r}}{\mathbf{-}}{{\mathbf{\rho }}}_{\mathbf{H}\mathbf{e}}{\mathbf{\right)}}{\mathbf{g}}}$ where FL is the lift force, V is the volume of the balloon, ρair is the density of air, ρHe is the density of helium, and g is the gravitational force.

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###### Problem Details

The density of helium gas is 0.179 kg/m3, while the density of air at sea level is 1.29 kg/m3, A research balloon needs to carry aloft a group of scientific instruments whose total mass is 324 kg. What is the minimum radius of the spherical balloon needed to overcome gravity at sea level? The mass of the balloon material when not inflated is an additional 15.0 kg.