Determine the mass of the envelope of a balloon hanging motionless at a height where the air density is 0.9 kg / m3.

Determine the mass of the envelope of a balloon hanging motionless at a height where the air density is 0.9 kg / m3. The ball is filled with gas with a density of 0.8 kg / m3. The volume of the ball is 600 m3.

Given:

ro1 = 0.9 kg / m3 – air density;

ro2 = 0.8 kg / m3 is the density of the gas with which the balloon is filled;

g = 10 Newton / kilogram – acceleration of gravity;

V = 600 cubic meters – the volume of the balloon.

It is required to determine m (kilogram) – the mass of the balloon shell.

Since, according to the condition of the problem, the balloon hangs motionless, the gravity acting on it is equal to the buoyant (Archimedean) force, that is:

F gravity = Farchimedes;

(m2 + m) * g = ro1 * g * V, where m2 is the mass of the gas with which the balloon is filled;

(ro2 * V + m) * g = ro1 * g * V;

ro2 * V + m = ro1 * V;

m = ro1 * V – ro2 * V;

m = V * (ro1 – ro2) = 600 * (0.9 – 0.8) = 600 * 0.1 = 60 kilograms.

Answer: the mass of the balloon shell is 60 kilograms.