1) IP A block of wood floats on water. A layer of oil is now poured on top of th

Question

1) IP 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.

If 95 % of the wood is submerged in water before the oil is added, find the fraction submerged when oil with a density of 870 kg/m3 covers the block.

Express your answer using two significant figures.

2) Find the pressure difference on an airplane wing if air flows over the upper surface with a speed of 116 m/s , and along the bottom surface with a speed of 106 m/s.

3) If the area of the wing is 35 m2 , what is the net upward force exerted on the wing?

Express your answer using two significant figures.

4.) Suppose an occlusion in an artery reduces its diameter by 17 % , but the volume flow rate of blood in the artery remains the same.

By what factor has the pressure drop across the length of this artery increased?

Express your answer using two significant figures.

Explanation / Answer

first

the density of water is 1000 kg/m^3
the density of air is 1.225 kg/m^3

M = 1000 * V * 0.95 + 1.225 * V * (1 - 0.95)

When the oil is added the new fraction (P) of the block submerged in water is given by

M = 1000 * V * P + 870 * V * (1 - P)

So
1000 * 0.95 + 1.225 * 0.05 = 1000 * P + 870 - 870 * P
P = 0.615
or
61.5% of the block will be below the water line (submerged in water), the rest will be above the water and will be in the oil layer.

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