A spherical weather balloon is filled with hydrogen until its radius is 4.00 m. Its total mass including the instruments it carries is 24.0 kg. (a) Find the buoyant force acting on the balloon, assuming the density of air is 1.29 kg/m3. kN (b) What is the net force acting on the balloon and its instruments after the balloon is released from the ground? kN (c) Why does the radius of the balloon tend to increase as it rises to higher altitude? Because the external pressure with increasing altitude.

a. F = 3389.09 N

b. Fₙ = 3153.89 N

Explanation:

The density of the air 1.29 kg / m³

Knowing the relation between the density and the volumen and the mass

ρ = m / V

m = ρ * V

m = ρ * ⁴/₃ π * r ³

m = 1.29 kg / m³ * ⁴/₃ π * (4.0m) ³ = 345 kg

The buoyant force is the weight of the air displaced

a.

F = m₁ * g

F = 345 kg * 9.8 m / s²

F = 3389.09 N

b.

F = m₂ * g

F = 24.0 kg * 9.8 m/s²

F = 235.2 N

F ₙ = 3389.09 - 235.2 = 3153.89 N

c. The balloon's radius increases with altitude because pressure decreases. that because the external pressure with increasing altitude