# The balloon, the shell mass of which is 1 g, is filled with hydrogen in a volume of 3 liters.

**The balloon, the shell mass of which is 1 g, is filled with hydrogen in a volume of 3 liters. The density of hydrogen is 0.1 kg / m3, air is 1.3 kg / m3. What is the lifting force of the ball? Express the answer in mN, take the acceleration of gravity equal to 10 N / kg.**

mo = 1 g = 1 * 10 ^ -3 kg.

V = 3 l = 3 * 10 ^ -3 m3.

ρ1 = 0.1 kg / m3.

ρ2 = 1.3 kg / m3.

g = 10 N / kg.

F under -?

The lifting force Fpod will be the difference between the buoyancy force of Archimedes Farch and the force of gravity Fт: Fпod = Farch – Fт.

The buoyancy force of Archimedes is determined by the formula: Farch = ρ2 * g * V. Where ρ is the density of air, g is the acceleration of gravity, V is the volume of the balloon.

Let us express the force of gravity Ft by the formula: Ft = (mo + V * ρ1) * g.

Fd = ρ2 * g * V – (mo + V * ρ1) * g = (ρ2 * V – mo – V * ρ1) * g = ((ρ2 – ρ1) * V – mo) * g.

Fd = ((1.3 kg / m3 – 0.1 kg / m3) * 3 * 10 ^ -3 m3 – 1 * 10 ^ -3 kg) * 10 N / kg = 0.026 N.

Answer: the lifting force of the ball is Fd = 0.026 N.