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

[TheStudent77888]

Homework Statement

[/B]
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?

Homework Equations

[/B]
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

 

[gneill]

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?

 

[TheStudent77888]

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?

Sorry, it was my first time posting.
I'll edit my post now with my attempts.

 

[mjc123]

So 1150kg-350kg = 800kg

Where do you get these figures from? I suspect 350 is a typo for 320, and you are confusing density with mass.