# 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).