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Homework Help: Volume of water a ship must displace to float

  1. Mar 28, 2012 #1
    1. The problem statement, all variables and given/known data
    What volume of water must a ship that masses 2.00x10^5 kg displace to float?

    2. Relevant equations
    density = mass/volume
    density of water = 1.00x10^3

    3. The attempt at a solution
    200,000/1000 = 200 m^3
    im guessing that in order to float you must displace your own volume. ive read other answer you have to displace your own mass
  2. jcsd
  3. Mar 28, 2012 #2
    Think of a free body diagram of a ship floating on water. There's a force from the weight of the ship, and since the ship isn't sinking or rising, the force of buoyancy from the water must equal that of the weight of the ship.
    The equation for buoyant force is: Fb=pfVfg
    In your case, pf is the density of water, and Vf is the volume of water displaced by the ship (your unknown variable.)
    Find the volume of displaced water which makes this buoyant force equal to the weight of the ship, and you're done. Hope this helps.
  4. Mar 28, 2012 #3
    so is it
    g*(2.00x10^5) = (1.00x10^3)*V*g
    g cancels
    V = 200,000/1000 = 200m^3
  5. Mar 28, 2012 #4
    Looks good. One thing you need to be sure of is your units on the water density. The density you used was in kg/m^3 which happens to be just what you needed for your problem to come to an answer of m^3. Always work through the units along with the numbers.
  6. Mar 28, 2012 #5
    ok thanks
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