# Buoyancy and ships/boats

1. Feb 14, 2009

### kazimmerman

1. The problem statement, all variables and given/known data
A boat with a density of 0.75 g/cc is floating in water. What percentage of the boat is floating above the surface of the water?

2. Relevant equations
I don't know any general formulas for buoyancy. I was hoping someone here could provide one.

3. The attempt at a solution
I understand that the density of water is 1 g/cc, so is it really as easy as understanding 1-0.75, or is that simply a coincidence. I know the answer is 25% and expected a rather low number due to the rather low density, but what is the exact procedure for solving this problem?

2. Feb 14, 2009

### mgb_phys

Every cc of boat in the water receives 1cc weight of water worth of pushing up.
So 1g/cc of flotation, if the boat weights 0.75g/cc then you get 0.25g/cc of overall flotation.

3. Feb 14, 2009

### Delphi51

That pretty much does it.
It would be clearer if you started with Fg = Fb
where the buoyancy force Fb = (mass of water displaced)*g.
The mass displaced is the density of water times the volume of water displaced.

4. Feb 14, 2009

### Dr.D

Draw a block partly submerged in the water, and use that at as a Free Body Diagram. Put the forces on it, a bouyant force and a weight force, and then set up the statics problem. Then work it out as Delphi51 says.

5. Feb 15, 2009

### kazimmerman

Thanks everybody. That was my line of thinking, but I wanted to be sure I wasn't mistaken.

6. Feb 15, 2009

### davieddy

As Archimedes is supposed to have said in his bath:
"Eureka"