Question

A hot-air balloon plus cargo has a mass of 308 kg and a volume of 2910 m3 on a day when the outside air density is 1.22 kg/m3. The balloon is floating at a constant height of 9.14 m above the ground.

Required:
What is the density of the hot air in the balloon?

Answer 1

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Answer:

1.114 kg/m³

Step-by-step explanation:

The total mass of the air in the balloon and the balloon + cargo will be the mass of the displaced air. If d is the density of the air in the balloon, then we have ...

2910d +308 = 2910×1.22

Solving for d, we find ...

2910d = 2919(1.22) -308

d = 1.22 -308/2910

d ≈ 1.114 . . . kg/m³

The density of the hot air is about 1.114 kg/m³.