# Archimedes' Principle

1. Nov 16, 2009

### G-reg

1. The problem statement, all variables and given/known data
A block of wood with volume V floats in water with 0.68V submerged. In oil the block floats with 0.86V of its volume submerged.

Find the density of the wood.

2. Relevant equations

$$\rho$$ = M/V

3. The attempt at a solution

I'm not really sure about how to attempt to solve this problem. I know the density of fresh water and that's about it. Can anyone help?

2. Nov 16, 2009

### ideasrule

Find the density of the WOOD, not of the oil? You don't need to know about the oil for that. Just draw a free-body diagram for the block of wood and write out Newton's second law.

3. Nov 17, 2009

### G-reg

Oh ok! I got it, thanks!

4. Nov 17, 2009

### G-reg

Ok I got the density of the wood but I could not find the density of the oil.

For the wood this is what I did..

density of water = 1 g/cm^3
and since the volume is .68 submerged then you divide the .68 by 1g/cm^3

but this method didn't work for the oil

5. Nov 17, 2009

### ideasrule

Dividing 0.68 by 1 only worked because the density of water happened to be 1 g/cm^3, and multiplying by 1 is equivalent to dividing by it. If the density was anything else, your method would have given the wrong answer.

If you're getting confused, you should really draw a free-body diagram and write out Newton's second law instead of trying to take shortcuts. FBD + Newton's second law is a simple, elegant, and intuitive way of approaching this problem that depends only on first principles. For this problem, draw two FBD's, one for the block when it's in oil and one for the block when it's in water. Then solve the equations.