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Homework Help: Density Problem

  1. Sep 18, 2012 #1
    1. The problem statement, all variables and given/known data

    A good estimate for the volume of a particular hot air balloon is 2800 m3. Suppose the total load (passengers, fuel, balloon fabric, etc.) on a hot air balloon is 724 kg. In preparing to launch, the pilot heats the air inside to an average temperature of 210 oC, giving it a density of 0.95 kg/m3 (compared to a density of 1.2 kg/m3 for the air outside the balloon). [Note! This means that the total mass of the hot air balloon is 724 kg plus the mass of the hot air in the balloon!]

    How much extra mass does the pilot need to keep in the basket in order to stay on the ground while all passengers are on board?

    2. Relevant equations

    3. The attempt at a solution

    I'm really lost here. Any help would be great.
  2. jcsd
  3. Sep 18, 2012 #2
    well so you want the balloon to stay on the ground, in other words: zero velocity

    this means that all the forces acting on the balloon need to sum up to be zero

    there's only going to be two forces acting on the balloon. The force due to gravity acting on the total mass of the system and the buoyancy force due to the difference in the density of the air inside the balloon compared to outside

    so obviously, as given in the problem, the 724 kg mass is not going to be enough to keep it down, so you need to add some other force to that to equal the buoyancy force
  4. Sep 18, 2012 #3
    -9.8(negative because pushing down)*724 + 9.8*___=0?
  5. Sep 19, 2012 #4
    well, no, you need to account for the buoyancy force
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