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Need help finding the buoyant force in this problem

  1. Apr 11, 2013 #1
    Hi everyone,

    This question is killing me, I don't know why but I just can't get my head around it.

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

    A team of 6 scouts plans to cross a lake on a raft they designed.

    The scouts have wooden beams with an average density of .80. The beams measure 30cm x 30cm x 3m.

    The average mass for the team members is 65kg, and for their safety, they want the top of the raft to be at least 3 cm above the surface of the water.

    How many beams will they need to complete their project successfully?

    2. Relevant equations

    I'm not sure if I need to post them. f = mg is the main one.

    3. The attempt at a solution

    My tutor gave me this method:

    Fg(scouts) = 65 x 9.8 x 6

    V(beam) = .27m^3

    Fg(beam) = 800 x 9.8 x .27

    Fg(raft) = Fg(beam) x n [n = number of beams]

    Fg(total) = Fg(scouts) + Fg(raft)

    Fb = 2381 x n

    Fb = Fg(total) = Fg(scouts) + Fg(raft).

    Solve for n.

    Now I'm just a lowly high school student so my math isn't all that great, and when I do this I end up getting 0. The equation as I write it out is

    2381n = -3822 - 2116n = -3822 - 2116n

    6713n = -3822 +3822

    6713n = 0

    Could anyone help me out with this question?

    Thanks,

    Kevin
     
  2. jcsd
  3. Apr 11, 2013 #2

    SteamKing

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    Your algebra has taken a wrong turn.

    Fg = -3822 - 2116n

    Fb = 2381n

    From statics, we know that Fb + Fg = 0 (there is no net force on a floating object)

    so, 2381n -3822 - 2116n = 0

    Solve for n
     
  4. Apr 11, 2013 #3

    haruspex

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    Try that step again.
     
  5. Apr 12, 2013 #4
    Thank you. You truly are the king of kings.
     
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