# How much weight can a 15 m³ balloon filled with hydrogen be able to lift?

**How much weight can a 15 m³ balloon filled with hydrogen be able to lift? Density of hydrogen – 0.09kg / m³, air – 1.29kg / m³**

V = 15 m3.

g = 9.8 m / s2.

ρw = 0.09 kg / m3.

ρ = 1.29 kg / m3.

P -?

mg -?

The ball, which is filled with hydrogen, is acted upon by 2 forces: the force of gravity m * g, directed vertically downward, and the buoyancy force of Archimedes Farch, directed vertically upward.

P = Farch – m * g.

m = V * ρv.

The buoyancy force of Archimedes Farch is determined by the formula: Farch = ρ * g * V. Where ρ is the density of the gas in which the body is immersed, g is the acceleration of gravity, V is the volume of the submerged part of the body.

P = ρ * g * V – V * ρw * g = (ρ – ρw) V * g.

P = (1.29 kg / m3 – 0.09 kg / m3) * 15 m3 * 9.8 m / s2 = 176.4 N.

P = mg * g.

mg = P / g.

mg = 176.4 N / 9.8 m / s2 = 18 kg.

Answer: a ball can lift a body with a weight of P = 176.4 N or a mass of mg = 18 kg.