<p>According to Archimedes\' principle, the mass of a floating object equals the

Question

<p>According to Archimedes' principle, the mass of a floating object equals the mass of the fluid displaced by the object. Use the principle to solve the following problems.<br />(a) A wooden cylinder 30.0cm high floats vertically in a tub of water (density = 1.00g/cm³). The top of the cylinder is 14.1cm above the surface of the liquid. What is the density of the wood?</p>
<p>(b) The same cylinder floats vertically in a liquid of unknown density. The top of the cylinder is 20.7cm above the surface of the liquid. What is the liquid density?</p>

Explanation / Answer

a) H = 30.0 cm, wa = 1.00 g/cm3, h = 14.1 cm, find the density of the wood wo

assume radius = r

the mass of a floating object = wo*r2H

the mass of the fluid displaced by the object = wa*r2(H - h)

wo*r2H  = wa*r2(H - h)

wo =  = wa(H - h)/H = 0.53 g/cm3

(b) h' = 20.7 cm, find the liquid density

the mass of a floating object = wo*r2H

the mass of the fluid displaced by the object = *r2(H - h')

wo*r2H  = *r2(H - h')

=  = wo*H/(H - h') = 1.71 g/cm3

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