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Homework Help: Buoyancy - Maximum mass a styrofoam sphere can hold in water.

  1. May 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Styrofoam has a density of . What is the maximum mass that can hang without sinking from a 20.0 -diameter Styrofoam sphere in water?
    Assume the volume of the mass is negligible compared to that of the sphere.

    2. Relevant equations
    FB = ρfVg
    Fg = mg

    3. The attempt at a solution
    So this is as far as I can get.
    The buoyancy force on the sphere is FB = ρfVg = 1000kg/m3 * pi * 0.22 * 9.8 = 333.54.
    However we need to take into account the weight of the sphere.
    The weight of the sphere = ρ*V = 300*pi*0.22 = 10.2
    This means the net weight on the sphere is Fnet = 333.54 - (10.2*9.8) = 233.54
    So the maximum weight that can be hung on the sphere must have a downward force of precisely that. mg = 233.54. m = 23.8kg.
    But apparently thats not it, any pointers?
  2. jcsd
  3. May 17, 2012 #2
    well first off, the DIAMETER is 20 cm
  4. May 17, 2012 #3
    Oh wow. Just a multitude of stupid mistakes!
    The diameter is 20cm so the radius is 10cm. AND the volume of a sphere is 4/3 pi r^3, I was doing the area of a circle.
    Argh, I'll hang my head in shame now.
  5. May 17, 2012 #4
    heh, don't worry, we all make mistakes like that

    I even saw one of my professors do the same thing in a lecture; he used the diameter instead of radius
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