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Buoyancy question -- A raft with different loads...

  1. May 17, 2017 #1
    1. The problem statement, all variables and given/known data

    A Raft with dimensions, 5m for length, 3m wide and 0.12m thick, is placed on water. The raft has a density of 320 kg/m^3.

    a) What volume of the raft is submerged into water, if the density of water is 1150 kg/m^3?

    b) A man and his elephant board the raft. How much of the raft is now submerged, if the mass of the man is 70kg and the elephant is 540kg?

    c) What is the maximum mass the raft can carry before it is totally submerged?

    2. Relevant Equations

    Volume of Raft = Length x Width x Height

    volume submerged =

    (Density of Raft)/(Density of Water) x Volume of raft

    Density = mass/volume


    3. Attempt at solution

    Volume of raft= 5x3x0.12 = 1.8m^3

    a)
    volume submerged= (320/1150)x1.8 = 0.5m^3

    b) Added weight= 540+70=610 kg

    old weight= 320x1.8= 576kg

    New weight = 1186kg

    New density= 1186/1.8= 659kgm^-3

    New Volume submerged = (659/1150)x1.8 = 1.03 m^3 submerged

    c) density must equal that of water before it is completely submerged.

    So 1150kg-350kg = 800kg, whichis the maximum mass the raft can carry



    Could someone have a look through if my equations and subsequent workings are correct?

    Thanks
     
    Last edited by a moderator: May 17, 2017
  2. jcsd
  3. May 17, 2017 #2

    gneill

    User Avatar

    Staff: Mentor

    There are two sections to the formatting template that you've missed. Helpers cannot help you until you've shown your own attempt at solution. How have you tried to solve the problem? What approaches have you tried? What equations from your course notes or textbook have you found that are relevant to this type of problem?
     
  4. May 17, 2017 #3
    Sorry, it was my first time posting.
    I'll edit my post now with my attempts.
     
  5. May 17, 2017 #4
    Where do you get these figures from? I suspect 350 is a typo for 320, and you are confusing density with mass.
     
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