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. Is the volume of wood submerged in water greater than, less than, or the same as before? more wood submerged in water than before less wood submerged in water than before same amount of wood is submerged in water as before If 92% of the wood is submerged in water before the oil is added, find the fraction submerged when oil with a density of 903 kg/m^3 covers the block. (Do not neglect the buoyant force of air before the oil is added.) 0.175 %

Explanation / Answer

Hi;

In this case we can solve this problem if we apply Archimedes' principle. Said principle establish the following:

f = [(p-p1)/(p2-p1)] ; where p is the density of the object, p1 is the density of the upper substance, p2 is the density of the lower substance and f is the fraction of the object which is under the lower substance.

The density of the water is 1000 kg/m3 while the average density of air is equal to 1.29 kg/m3.

(a) At the beginning the block floats over the water, so air and water are the two substances and the fraction would be equal to:

f = [p - p(air)]/[p(water) - p(air)]

If then we add oil over the object in a way the object is between both substances we have that the new fraction would be equal to:

f' = [p - p(oil)]/(p(water) - p(oil)]

It is difficult to predict if the block would be submerged greater or less than before when we add the oil. This is due to two effects that compete. As we know p(oil) > p(air) but p(oil) < p(water) therefore when we put oil the numerator of f' is smaller than the one of f, but the denominator of f' is also smaller.

A way to answer this question would be to use the value of p(oil) given in the second question and compare the value of f and f'.

0.92 = ( p - 1.27) /(1000 - 1.27) :::::: p = 920 kg/m3

f' = [p - p(oil)]/[p(water) - p(oil)] =[(920 - 903)/(1000 - 903)] 0.175

As f' (0,175) is smaller than f(0.92) we have to conclude that when we add the oil, the wood will be less submerged in water than before.

(b) This question was previously answered, because the density of the air was not neglected when we calculated the density of the wood. Therefore, the answer would be:

f(%) = 17.5 %

I hope it helps.

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