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Homework Help: Archimedes' principle

  1. Sep 11, 2010 #1
    1. The problem statement, all variables and given/known data

    A rectangular waterproof air mattress is 2.0m long, 0.50mwide and 0.08m thick. It has a mass of 2.0kg and is supporting an additional mass of m, while floating in the water,
    calculate the mass, m, assuming the density of water is 1000kg/m^3 and density of air is 1.29kg/m^3

    2. Relevant equations

    B = weight of displaced fluid

    B= density of water x volume * g

    where B = mass of 2kg, unknown mass and mass of air

    3. The attempt at a solution

    I solved it and i got 78.1kg. The answer is 79.9kg

    this is what i did:

    m1g + m2g + density(air) * V *g = density(water) * V * g

    solve for m2:

    m2 = density(water) * V - density(air) * V - m1
    m2 = 1000(0.08) - 1.29(0.08) - 2
    m2 = 78.1kg

    Can someone point out where i went wrong????
     
  2. jcsd
  3. Sep 11, 2010 #2

    Borek

    User Avatar

    Staff: Mentor

    No idea how to get answer that you listed as correct, IMHO it is off by 2 kg, but

    this is just incorrect. Perhaps you have rounded down intermediate results, or just keyed those numbers wrong in your calculator.

    800 - 0.1032 - 2 = 77.8968 ≈ 77.9
     
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