Question

A hot air balloon has a volume 3,223 m³ . It is filled with hot air of density 0.96 kg/m 3 . The total mass of cabin, envelope etc is 350 kg. Find the maximum load of the balloon in Newtons if the density of surrounding air is 1.29kg/ m³

Use g = 9.8 m/s² Calculate answer to one decimal.

Answer 1

According to Archimedes principle, the weight of a floating body is exactly equal to the amount of fluid displaced by the body in that fluid (liquid or gas). For the body to remain afloat and at rest, the buoyant force or upward thrust on the body must be exactky equal to the net weight of the body.

In the case of this problem, we can see that the density of hot air is lesser than that of the surrounding air and hence, it results in a buoyant force which is more than the weight of the displacing balloon, resulting in the balloon moving upwards.

As per problem statement,

Effective mass of balloon = M_B = 3223 * (1.29 - 0.96) = 1063.59 kg

Mass of other accessories = M_O = 350 kg

Thus, effective mass M_E = M_B + M_O = 1413.59 kg

Hence, effective buoyant force acting on balloon and its accessories = F_B = M_E * g = 1413.59 * 9.8 = 13853.182 N

Or, F_B = 13853.2 N (rounded upto one decimal place)

Therefore, the maximum load of the balloon = 13853.2 Newtons.