If 80% of a piece of wood is submerged in water before oil is added, find the fraction submjerged when oil with a density of 781 kg/m^3 covers the block. (Don't neglect the buoyant force of air before the oil is added).

I thought to find the density of wood by setting the % submerged to density of wood/density of fluid (water). Then I was going to use the same equation, now using that found density of the wood and substituting the density of the oil for the fluid, but that method gives me over 100% submerged, which can't be right. Any suggestions?

Here are the facts: An object displaces fluid, a bouyant force is created that equals the weight of the displaced fluid.

Before oil:
bouyant force= .8*volume*densitywater + .2*volume*densityair
of course this is equal to the weight of the wood.
After oil:
bouyant force= x*volume*densitywater + (1-x)*volume*density oil. This again equals the weight of the block.

Set the two weights equal. Solve for x


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