A block of wood floats on water. A layer of oil is now poured on top of the wate

Question

A block of wood floats on water. A layer of oil is now poured on top of the water to a depth that more than covers the block, as shown in the figure(Figure 1) .

Is the volume of wood submerged in water greater than, less than, or the same as before?

Is the volume of wood submerged in water greater than, less than, or the same as before?

If 94 % of the wood is submerged in water before the oil is added, find the fraction submerged when oil with a density of 875 kg/m3 covers the block.

Express your answer using two significant figures.

Explanation / Answer

a)

the block is submerged in less water than before because the oil provides additional buoyant force

b)

before oil is added

Fb = pw * Vsubmerged g

note that this is the weight of the wood

after oil is added :

let fw = fraction of block in water

foil = fraction of block in oil

substitute

Fbw + Fboil = Fb

pw * Vinwater g + poil Vinoil g = 0.94 * pw * Vtotal g

pw * fw Vtotal + poil * foil * Vtotal = 0.94 * pw * Vtotal

pw * fw + poil * ( 1 - fw) = 0.94 * pw

fw * (pw - poil) = 0.94 * pw - poil

fw = 0.94 * pw - poil / (pw - poil)

fw = 0.94 * 1000 - 875 / ( 1000 - 875)

fw = 0.52

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