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Buoyant forces

  1. Jul 8, 2010 #1
    1. The problem statement, all variables and given/known data
    A 63 kg survivor of a cruise line disaster rests atop a block of Styrofoam insulation, using it as a raft. The Styrofoam has dimensions 2.00 m multiplied by 2.00 m multiplied by 0.04 m. The bottom 0.026 m of the raft is submerged.

    Write Newton's second law for the system in one dimension, using B for buoyancy, w for the weight of the survivor, and wr for the weight of the raft. (Set a = 0. Use w for w, and w_r for I>wr as needed)

    Calculate the numeric value for the buoyancy, B. (Seawater has density 1025 kg/m3.)


    3. The attempt at a solution
    Fy: B-w-w_r

    I need to calculate the weight of the raft. the only thing that I could think to do, given the values in the problem, was to use density=m/v
    1025 kg/m3 = m/0.16m3
    m=164kg (this seems way to high to be the mass of Styrofoam)

    (I got the volume by multiplying the dimensions of the raft)

    B= 63kg-164kg
    B=101 kg
     
  2. jcsd
  3. Jul 8, 2010 #2

    Doc Al

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    Staff: Mentor

    Why? I thought you just needed to calculate the buoyant force?
     
  4. Jul 8, 2010 #3
    I do, but I figured that, since I was asked to provide the equation for Fy (B-w-w_r), I would need to use that. Is this not the case?

    I know:
    V = 0.16 m3
    ΔV = 0.026 m
    m = 63 kg

    In order to use the bulk modulus, I need to know P. Do i just use P for water?
     
  5. Jul 8, 2010 #4

    Doc Al

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    Staff: Mentor

    No, you don't need that to solve for the buoyant force. (But you'll need it to solve for the mass of the raft, if they ask that later.)

    B is the buoyant force, not the bulk modulus. You are given the density of seawater. You'll need that and Archimedes' principle.
     
  6. Jul 8, 2010 #5
    i just found another equation for B that my prof gave me. It is B=ρVg.
    B=(1025 kg/m3)(0.16m3)(9.8m/s2)
    B=1607.2N

    this is wrong though
     
  7. Jul 8, 2010 #6

    Doc Al

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    Staff: Mentor

    That's Archimedes's Principle--B is the buoyant force.
    You're using the wrong volume. What's the volume of displaced fluid?
     
  8. Jul 8, 2010 #7
    the volume I used was the volume of the block. when it is put in the water, 0.026m of it is submerged. does this mean that i need to subtract this value from the volume of the block?
     
  9. Jul 8, 2010 #8

    Doc Al

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    0.026m is the depth which is submerged. What's the volume that's submerged?
     
  10. Jul 8, 2010 #9
    the only equation in my textbook i can find shows this:

    ρobject / ρfluid = Vfluid / Vobject
     
  11. Jul 8, 2010 #10
    i just figured it out.
    2m x 2m x 0.026m = 0.104m3
     
  12. Jul 8, 2010 #11
    Using the value of B and the weight w of the survivor, calculate the weight wr of the Styrofoam.
    B=w + w_r
    1044.68N = 617.4N + w_r
    w_r = 427.3 N


    What is the density of the Styrofoam?
    ρ=m/v
    ρ=(43.6 kg) / 0.16 m3
    ρ=272.5 kg/m3


    What is the maximum buoyant force, corresponding to the raft being submerged up to its top surface?
    B=ρvg
    B=(1025 kg/m3)(0.16m3)(9.8 m/s2)
    B=1607.2 N


    What total mass of survivors can the raft support?
    which equation can I use for this?
     
  13. Jul 8, 2010 #12

    Doc Al

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    Staff: Mentor

    Use the same force equation. Only you have a new value for B and you're solving for w.
     
  14. Jul 8, 2010 #13
    okay, i was just using the wrong buoyancy force. Thanks! :)
     
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