A raft is constructed of wood having a density of 600 kg/m3. It's surface area is 5.70 m2 and its volume is 0.60 m3. Find the depth that the raft sinks when it is placed in fresh water. How can you solve this problem using mass?

Question

anonymous · Answer

Buoyancy formula! P = m/v ; mass density = mass/volume. You can start with that!

anonymous · Answer

ops I meant mass density

anonymous · Answer

Get its weight from density times volume.
Get its thickness from volume divided by surface area.

It floats when it displaces a volume of water that has a weight
equal to the raft's weight, so figure how much of the thickness will be under water.

The density of water is 1000kg per m3.

mrnood · Answer

I'm not convinced that the question has sufficient information for a solution.

The mass is easy to derive (0.6*600 = 360kg)

It will float therefore at the point where its shape displaces 360 kg water (i.e. 360 litres)

However - the SHAPE of the structure is not given. It is possible to construct a cylinder, a cube, a cuboid, a tetrahedron, each of which could have the stated 'surface area' and each of which would float at different depths to displace the required mass of water.

Also - what does 'surface area' mean - are we to assume a solid body - with 1 surface - or shell or boat shape with inner and outer surfaces. Either of these could be designed to meet the mass and area specified - but each shape would float at different depths.

On top of this - even for a given shape - the 'depth' would depend on its orientation in the water.

All in all this is an ill- phrased question and appears to be unanswerable in its given form.

anonymous · Answer

Conventionally, a raft is a flat rectangular solid. Safe to assume that here.

mrnood · Answer

Unless the term 'raft' has a truly conventional meaning within this context (i.e. the student is taught that a raft is a solid rectangular block) then I think the question should be more explicit.

I will have to check whether the area and SA are sufficient to define the cuboid's dimensions uniquely. 
Or maybe the question means the 'plan area' - in which case the depth IS easily determined. Not a well phrased question in any case.

mrnood · Answer

On the above assumptions - Plan area = 5.7m^2
We need a submerged volume = 360l (= 0.360m^3)
So submerged depth = 0.36/5.7 m = 0.063m or 63mm

anonymous · Answer

Yes, to make the question clear, it should have indicated
the raft was rectangular solid with length and width and either
thickness or volume specified.