Question

A helium filled balloon is spherical with a radius of 10.0 meters. Assume that the balloon envelope and gondola together have a mass of 2000 kg.

a: what is the bouyant force on the balloon and gondola?

b: how much additional weight can be lifted by the balloon (the payload)? (don't forget the weight of the helium)

Answer 1

(a) Radius of the balloon, r = 10.0 m

So, volume of the balloon, V = (4/3)*pi*r^3 = (4/3)*pi*10.0^3 = 4188 m^3

You can take the density of air as 1.2 kg/m^3 by consulting your text book.

So, buoyant force = weight of the displaced volume of air = V x density of air x g

= 4188 x 1.2 x 9.81 = 49301.14 N

(b) Mass of the envelope and gondola = 2000 kg

Density of helium = 0.18 kg/m^3

So, weight of envelope and gondola and helium = 2000*g + 0.18*V*g

= 2000*9.81 + 0.18*4188*9.81 = 27015.17 N

Therefore, the additional weight that can be lifted by the balloon = 49301.14 - 27015.17 = 22285.97 N (Answer)