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

In summary: The density of the raft is 320 kg/m^3, but this does not mean that the raft itself weighs 320 kg. It means that for every 1 m^3 of the raft, it weighs 320 kg. So to find the mass of the raft, you need to multiply the density by the volume, which gives you 320 kg/m^3 x 1.8 m^3 = 576 kg. Similarly, the density of water is given as 1150 kg/m^3, but this does not mean that 1 m^3 of water weighs 1150 kg. It means that for every 1 m^3 of water, it weighs 1150 kg. To find the mass of the
  • #1
TheStudent77888
2
0

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
 
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  • #2
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?
 
  • #3
gneill said:
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.
 
  • #4
TheStudent77888 said:
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.
 

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

How does the weight of the load affect the buoyancy of the raft?

The weight of the load directly affects the buoyancy of the raft. The more weight that is added to the raft, the lower it will sit in the water, reducing its buoyancy.

How can the buoyancy of the raft be increased?

The buoyancy of the raft can be increased by either decreasing the weight of the load or increasing the volume of the raft. This can be achieved by adding more air to the raft or using materials that are less dense.

Will the buoyancy of the raft change with the distribution of the load?

Yes, the buoyancy of the raft will change with the distribution of the load. If the load is evenly distributed, the raft will have a more balanced buoyancy. However, if the load is unevenly distributed, the raft may tilt and have less buoyancy on one side.

How does the shape of the raft affect its buoyancy?

The shape of the raft can greatly affect its buoyancy. A wider and flatter raft will have more surface area and therefore more buoyancy compared to a narrower and taller raft with the same weight and load.

Can the buoyancy of the raft be affected by external factors?

Yes, the buoyancy of the raft can be affected by external factors such as waves, wind, and currents. These external forces can cause the raft to shift and affect its buoyancy, potentially causing it to sink or capsize.

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