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.