The mass of the balloon shell is 210 kg. Inflated with helium, it can lift a load of 110 kg
| May 9, 2021 | education
The mass of the balloon shell is 210 kg. Inflated with helium, it can lift a load of 110 kg, while the density of helium is 0.18 kg / m ^ 3, and the density of air is 1.29 kg / m ^ 3. Find: volume
mo = 210 kg.
mg = 110 kg.
g = 10 m / s2.
ρg = 0.18 kg / m3.
ρw = 29 kg / m3.
V -?
To evenly lift the balloon, the gravity of the balloon with the load
(mo + mg + ρg * V) * g should be equal to the buoyancy force of Archimedes Farch: (mo + mg + ρg * V) * g = Farch.
The buoyancy force of Archimedes Farch is expressed by the formula: Farch = ρw * V * g.
(mo + mg + ρg * V) * g = ρw * V * g.
mo + mg + ρg * V = ρw * V.
V = (mo + mg) / (ρv – ρg).
V = (210 kg + 110 kg) / (29 kg / m3 – 0.18 kg / m3) = 11.11 m3.
Answer: the balloon has a volume of V = 11.11 m3.
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