# The volume of the balloon shell is 200 meters cubed. The ball pulls the cable, by which it is attached

The volume of the balloon shell is 200 meters cubed. The ball pulls the cable, by which it is attached to the mooring mast, with a force of 400 N. After the cable is released, the ball soars at a certain height. What is the density of the air at this altitude?

Data: Vob – volume of the sphere shell (Vob = 200 m3); Fpod – lifting force (Fpod = 400 N).

Const: g – acceleration due to gravity (g ≈ 9.8 m / s2); ρв1 – air density at the mast (assumed standard value ρв1 = 1.225 kg / m3).

1) The ball is attached to the mast: Fp = FA1 – Ft and Ft = FA1 – Fp.

2) The ball is hovering: FA2 = Ft = FA1 – Fpod.

ρv2 * g * Vob = ρv1 * g * Vob – Fd.

ρw2 = (ρw1 * g * Vob – Fd) / (g * Vob).

Let’s perform the calculation: ρw2 = (ρw1 * g * Vob – Fd) / (g * Vob) = (1.225 * 9.8 * 200 – 400) / (9.8 * 200) ≈ 1.021 kg / m3.

Answer: The air density at the height of the ball is 1.021 kg / m3 (* at g ≈ 10 m / s2 and ρw1 = 1.29 kg / m3, the density will be ρw2 = 1.09 kg / m3). One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.