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Buoyancy Problem

  1. Jan 1, 2008 #1
    1. The problem statement, all variables and given/known data

    An empty rubber balloon has a mass of .0120 kg. The balloon is filled with helium at a density of .181 kg/m^3. At this density the balloon is spherical with a radius of .500m. If the filled balloon is fastened to a vertical line, what is the tension in the line?

    2. Relevant equations

    Equations that I found:
    volume of a sphere = 4/3(pi)(r^3)
    density = mass/volume
    Buoyant force = weight

    3. The attempt at a solution

    I attempted to set up a free body diagram, with two forces. One is the tension going up, and the other is weight going down. That would mean T = mg. since density = mass/volume, .181 kg/m^3 = mass / (4/3)(pi)(.5)^3. That gets a mass of .095g.
    .095g(9.8 m/s^2) = .929 N. The correct answer is 5.57 N. So, I got it wrong.
     
  2. jcsd
  3. Jan 1, 2008 #2

    Doc Al

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    Staff: Mentor

    The balloon floats--the string tension pulls the balloon down. What other forces act on the balloon?

    Note: Buoyant force = weight of displaced fluid
     
  4. Jan 1, 2008 #3
    pressure?
     
  5. Jan 1, 2008 #4

    Doc Al

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    Staff: Mentor

    The pressure of the air is a force per unit area. The resultant force due to the air pressure is the buoyant force.

    So far we have two forces acting on the balloon: tension and buoyant force. What's the third force?
     
  6. Jan 1, 2008 #5
    gravity?
     
  7. Jan 2, 2008 #6

    Doc Al

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    Staff: Mentor

    Right! The weight of the balloon is the third force.

    So write an expression for the net force and use it to solve for the tension.
     
  8. Jan 2, 2008 #7
    But what is the equation for buoyancy, if there is no displaced fluid in the problem?
     
  9. Jan 2, 2008 #8

    Doc Al

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    Staff: Mentor

    Sure there is: the displaced fluid is the air! It's the air that exerts the buoyant force on the balloon.
     
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