Question

A 6.85-m radius air balloon loaded with passengers and ballast is floating at a fixed altitude. Determine how much weight (ballast) must be dropped overboard to make the balloon rise 114 m in 17.0 s. Assume a constant value of 1.2 kg/m3 for the density of air. Ballast is weight of negligible volume that can be dropped overboard to make the balloon rise.

Answer 1

Answer: 120 kg

Explanation:

Given

Radius of balloon, r = 6.85 m

Distance moved by the balloon, d = 114 m

Time spent in moving, t = 17 s

Density of air, ρ = 1.2 kg/m³

Volume of the balloon = 4/3πr³

Volume = 4/3 * 3.142 * 6.85³

Volume = 4/3 * 3.142 * 321.42

Volume = 4/3 * 1009.90

Volume = 1346.20 m³

Density = mass / volume ->

Mass = Density * volume

Mass = 1.2 * 1346.2

Mass = 1615.44 kg

Velocity = distance / time

Velocity = 114 / 17

Velocity = 6.71 m/s

If it starts from rest, 0 m/s, then the final velocity is 13.4 m/s

acceleration = velocity / time

acceleration = 13.4 / 17 m/s²

The mass dropped from the balloon decreases Mb and increases buoyancy

F = ma

mg = (Mb - m) * a

9.8 * m = (1615.44 - m) * 13.4/17

9.8m * 17/13.4 = 1615.44 - m

12.43m = 1615.44 - m

12.43m + m = 1615.44

13.43m = 1615.44

m = 1615.44 / 13.43

m = 120.29 kg