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Fluid Mechanics of helium-filled balloon

  1. Nov 18, 2003 #1

    I would really appreciate help in solving the following problem.

    A helium-filled balloon is tied to a 2.00 m long, 0.050 kg uniform

    string. The balloon is spherical with a radius of 0.400 m. When

    released, the balloon lifts a length h of string and then remains in

    equilibrium. The envelope of the balloon has a mass of 0.250 kg.

    What is the value of h?
  2. jcsd
  3. Nov 19, 2003 #2


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    Staff Emeritus
    Science Advisor

    Since 2 meters of the uniform string as mass 0.05 kg, h meters of the string will have mass (h/2)(0.05)= 0.025h kg and so weight 0.025 gh= 0.245h Newtons. The balloon itself has mass 0.25 kg and so
    weight 0.25*g= 2.45 Newtons so the balloon is lifting 2.45+ 0.245h Newtons. You will need to use the bouyancy of helium (the baloon contains (4/3)(pi)(0.43= 0.268 m3 of helium) to determine how much weight the balloon can lift and so what h is.
  4. Nov 19, 2003 #3
    Hello again,

    Is the following formula the one I should use to find the buyoancy of helium?

    B_helium = p_helium * V_helium * g

    Also will the combined weight of string and balloon equal the buyoancy of helium at height h?

    I really appreciate your help.
  5. Nov 19, 2003 #4

    Doc Al

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    Staff: Mentor

    Your formula will give you the weight of the helium.

    For equilibrium, the forces must balance. The forces acting down are the weights of the balloon envelope, the helium, and the length (h) of string. These must be balanced by the bouyant force acting upward, which equals the weight of the displaced air.
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