How much weight can a 60 m3 balloon filled with helium lift if the mass of its shell is 20?

V = 60 m3.

mob = 20 kg.

ρg = 0.178 kg / m3.

ρw = 1.29 kg / m3.

g = 9.8 m / s2.

m -?

Two forces act on the balloon filled with helium in the air: the force of gravity Ft, directed vertically downward, and the buoyancy force of Archimedes Farkh, directed vertically upward.

The force of gravity is determined by the formula: Ft = mw * g, where mw is the mass of the ball with helium, g is the acceleration of gravity.

msh = mob + V * ρg.

Ft = (mob + V * ρg) * g.

Ft = (20 kg + 60 m3 * 0.178 kg / m3) * 9.8 m / s2 = 300.7 N.

The buoyancy force of Archimedes Farch is determined by the formula: Farch = ρw * g * V. Where ρ is the density of air, g is the acceleration of gravity, V is the volume of the ball.

Farch = 1.29 kg / m * 9.8 m / s2 * 60 m3 = 758.5 ​​N.

m * g = Farch – Fт.

The mass of the load m, which can be lifted by the balloon with helium, is expressed by the formula: m = (Farch – Ft) / g.

m = (758.5 ​​N – 300.7 N) / 9.8 m / s2 = 46.7 kg.

Answer: a balloon with helium can lift a weight of m = 46.7 kg.