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A hot air balloon with a total mass of 480 kg, including passengers and 1 kg sandbags, is floating steadily at a height of 100 m. The balloon's buoyancy is determined by its fixed volume, V. If N sandbags are removed, the balloon ascends to a stable height of approximately 150 m. The air density changes with altitude according to ρ(h) = ρ₀e⁻ʰ/ʰ₀, where ρ₀ = 1.25 kg/m³ and h₀ = 6000 m. What is the value of N?
- 2
- 4
- 6
- 8
Correct answer: 4
Solution
The change in height of the balloon corresponds to a change in buoyant force due to the varying air density. Removing 4 sandbags reduces the total mass, allowing the balloon to reach a new equilibrium height of 150 m, as calculated using the density-altitude relationship.
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