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:

$\overline{){{\mathbf{F}}}_{{\mathit{L}}}{\mathbf{=}}{\mathbf{V}}{\mathbf{(}}{{\mathbf{\rho}}}_{\mathbf{a}\mathbf{i}\mathbf{r}}{\mathbf{-}}{{\mathbf{\rho}}}_{\mathbf{H}\mathbf{e}}{\mathbf{)}}{\mathbf{g}}}$ where F_{L} is the lift force, V is the volume of the balloon, ρ_{air} is the density of air, ρ_{He} is the density of helium, and g is the gravitational force.

The density of helium gas is 0.179 kg/m^{3}, while the density of air at sea level is 1.29 kg/m^{3}, 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.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Buoyancy & Buoyant Force concept. You can view video lessons to learn Buoyancy & Buoyant Force. Or if you need more Buoyancy & Buoyant Force practice, you can also practice Buoyancy & Buoyant Force practice problems.