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Math Help - [SOLVED] Physics questions, air buoyancy and volume

  1. #1
    Newbie haflore's Avatar
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    [SOLVED] Physics questions, air buoyancy and volume

    For this set of questions I don't need answers, per se, what I need is a little help figuring out where to begin to work them out.

    1st question is: The density of air near the earth's surface is 1.29Kg/m^3. If a helium balloon with a mass of 1Kg floats in the air without rising or falling, what is the volume of the balloon? Show your working(presume that the mass of the material of the balloon is negligible).

    2nd: A balloon filled with 1lt of air is 70kPa, what would be the volume of the balloon when it reaches sea level? Show your calculations.

    Many thanks.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by haflore View Post
    For this set of questions I don't need answers, per se, what I need is a little help figuring out where to begin to work them out.

    1st question is: The density of air near the earth's surface is 1.29Kg/m^3. If a helium balloon with a mass of 1Kg floats in the air without rising or falling, what is the volume of the balloon? Show your working(presume that the mass of the material of the balloon is negligible).

    2nd: A balloon filled with 1lt of air is 70kPa, what would be the volume of the balloon when it reaches sea level? Show your calculations.

    Many thanks.
    For the first, note that the buoyant force is equal to the volume of the displaced fluid (in this case air.) So in order for the balloon the "just float" the weight of the Helium must be equal to the weight of the air that would be contained in a volume of the size of the balloon.

    For the second, remember Boyle's Law:
    P_1V_1 = P_2V_2

    -Dan
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  3. #3
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    1) For the first one use Archemedes Principle (The Buoyant Force is Equal to the weight of the fluid displaced, in this case air)

    so in this case the force would be 1.29 kg m^{-3} \times V

    equate that to the weight of the balloon and out pops the answer

    2) For the second one I assume your familiar with the fact that for an ideal gas
    pV=nRT

    in this case we assume the temperature remains constant and we know the number of moles of gas inside the balloon is constant so that simplifies down to p \propto \frac{1}{V} or p=\frac{k}{V}

    use the first set of values to find k then plug in the pressure at sea level (a quick google gives me it as 101kPa to 3sf) to find the volume

    or you could do it the other way I can just never remember all the different gas laws so I just remember pV=nRT much easier!
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