Air is a fluid and our bodies displace air. And so, a buoyant force is acting on each of us. Estimate the magnitude of the buoyant force on a \(75-\mathrm{kg}\) person due to the air displaced.

THINKING IT THROUGH. The key word here is estimate because not much data is given. We know that the buoyant force is \(F_{\mathrm{b}}=ho_{\mathrm{a}} g V\), where \(ho_{\mathrm{a}}\) is the density of air (which can be found in Table 9.2), and \(V\) is the volume of the air displaced, which is the same as the volume of the person. The question is, how do we find the volume of the person?

The mass is given, and if the density of the person were known, the volume could be found \((ho=m / V)\) or \(V=m / ho\). Here is where the estimate comes in. Most people can barely float in water, so the density of the human body is about that of water, \(ho=1000 \mathrm{~kg} / \mathrm{m}^{3}\). Using this estimate, the buoyant force can also be estimated.

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TABLE 9.2 Densities of Some Common Substances (in kg/m) Solids Density (p) Liquids Density (p) Density Gasesa (p) Aluminum 2.7 10 Alcohol, ethyl 0.79 10 Air 1.29 Brass 8.7 x 10 Alcohol, methyl 0.82 10 Helium 0.18 Copper 8.9 x 103 Blood, whole 1.05 x 103 Hydrogen 0.090 Glass 2.6 x 103 Blood plasma 1.03 10 Oxygen 1.43 Gold 19.3 x 103 Gasoline 0.68 x 10 Water vapor 0.63 (100C) Ice 0.92 x 103 Kerosene 0.82 10 Iron, steel 7.8 10 Mercury 13.6 10 Lead 11.4 103 Seawater (4C) 1.03 10 Silver 10.5 x 103 Water, fresh 1.00 x 10 (4C) Wood, oak 0.81 10 a At 0C and 1 atm, unless otherwise specified.