A hot air balloon is a sphere of volume 2210 m3. The density of the hot air inside is 1.13 kg/m3. The balloon itself has a mass of 240 kg.

Question

What is the total net force acting on the balloon?

Answer 1

The net force on the balloon is the sum of the gravitational force and the buoyant force.

The gravitational force is the weight of the balloon plus the weight of the air: F_g = -g(m + ρ_hotV), where ρ_hot is the density of hot air inside the balloon and V is the volume of the balloon.

The buoyant force is equal to the weight of the air displaced by the balloon: F_b = gρ_standardV, where ρ_standard is the density of the air surrounding the balloon.

Thus, our net force is -g(m + ρ_hotV) + gρ_standardV = gV(ρ_standard-ρ_hot)-mg = 9.8*2210(1.29-1.13)-9.8*240 = 1114 N.

Answer 2

Total net force F = Dvg - (m +D_hotV)g = (D - D_hot)Vg - mg= (1.29 - 1.13)·2210·9.81 - 240·9.81 = 1114.42 N