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Homework Help: Density and Volume

  1. Aug 8, 2010 #1
    1. The problem statement, all variables and given/known data
    A balloon is to be filled with helium(density = 0.178kg/m^3) while the air outside has density of 1.29km/m^3. The mass of the empty balloon is 80.0kg and it is to lift a load of 240kg. What minimum volume is necessary for the lift off? Assume that the balloon material and the load occupy negligible volumes.


    2. Relevant equations

    density = M/V

    3. The attempt at a solution

    I'm not quite sure how to start with this question. Can someone help me please?
     
  2. jcsd
  3. Aug 8, 2010 #2

    rl.bhat

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    The balloon will float when the weight of the displaced air is equal to the weight of the balloon with load.

    Volume of the balloon = mass of the balloon/density of helium.
     
  4. Aug 8, 2010 #3
    hmmm. not quite getting it.

    This is archemides' principle right? so wouldn't the equation be:

    density of balloon/ density of gas = volume of gas/ volume balloon??
     
  5. Aug 8, 2010 #4

    rl.bhat

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    Mass of the displaced air = Ma = (240 + 80 + VHe* ρHe) kg.

    volume of the air = Ma/ρa = ...... = Volume of the balloon.

    So Vb*ρa = (240 + 80 + VHe* ρHe) kg

    Ηere volume of the balloon is equal to the volume of He.
     
  6. Aug 8, 2010 #5
    k...just want to clarify. The balloon will float when the mass of the displaced air is equal to the weight of the balloon plus the load.

    therefore,
    Ma = (240 + 80)kg including helium??

    how come is volume of air = volume of balloon?

    sorry...a bit confused. I'm not great with this kind of physics.
     
  7. Aug 9, 2010 #6

    rl.bhat

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    (240 + 80)Kg is mass with out helium. Mass of the displaced air is equal to the (mass of helium + 240 + 80) kg. Balloon will float only when it is filled with the helium. Since the balloon material and the load occupy negligible volumes, volume of the helium = volume of the air.
     
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