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## Homework Statement

A block of wood floats in fresh water with 0.722 of its volume V submerged and in oil with 0.895 V submerged. Find the density of (a) the wood and (b) the oil.

## Homework Equations

mass = density x volume

f = ma

conservation of mass

[itex]F_{weight} - F_{buoyancy} = 0 [/itex] when an object floats on the surface of a fluid.

density of water = [itex]1000 \frac{kg}{m^3}[/itex]

## The Attempt at a Solution

[itex]ρ_{wood}(V)g - ρ_{water}(.722V)g = m\cdot0 [/itex] when the block floats

so

[itex]ρ_{wood}(V)g = ρ_{water}(.722V)g [/itex]

and

[itex]ρ_{wood} = ρ_{water}\frac{(.722V)g}{(V)g} [/itex]

we know density of water = [itex]1000 \frac{kg}{m^3}[/itex] so

[itex]ρ_{wood} = 1000(.722) = 722 \frac{kg}{m^3} [/itex]

Can you confirm that this looks correct? I've been waiting for a chance to practice with LaTeX and decided to jump in with this problem. I appreciate your time.