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 Figure 15-30.

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

b) If 94% of the wood is submerged in water before the oil is added, find the fraction submerged when oil with a density of 909 kg/m3 covers the block. (Do not neglect the buoyant force of air before the oil is added.)

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 Figure 15-30. 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 909 kg/m3 covers the block. (Do not neglect the buoyant force of air before the oil is added.)

Explanation / Answer

a)The block is submerged in less water than before because the oil provides additional buoyant force.

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b) Fw = fraction of block in water

Foil = fraction of block in oil

Fb,w + Fb,oil = Fb

Pw V(in water) g + Poil V(in oil) g = 0.94 Pw Vtotal g

Pw Fw Vtotal + Poil Foil Vtotal = 0.94 Pw Vtotal

Fw ( Pw - Poil ) = 0.94 Pw - Poil

Fw = 0.94Pw - Poil / (Pw - Poil)

= 0.94(1000) - 909 / (1000 - 909)

= 0.34

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