Ask Question
6 July, 09:15

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.

+5
Answers (1)
  1. 6 July, 09:21
    0
    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
Know the Answer?
Not Sure About the Answer?
Find an answer to your 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 ...” in 📗 Physics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers