Calculating Average Density: Floating Woman

Strategy

We can find the woman’s density by solving the equation

fraction submerged = \frac{{\bar{ρ}}_{obj}}{ρ_{fl}}

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for the density of the object. This yields

{\bar{ρ}}_{obj} = {\bar{ρ}}_{person} = (fraction submerged) \cdot ρ_{fl} .

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We know both the fraction submerged and the density of water, and so we can calculate the woman’s density.

Solution

Entering the known values into the expression for her density, we obtain

{\bar{ρ}}_{person} = 0 . 970 \cdot (10^{3} \frac{kg}{m^{3}}) = 970 \frac{kg}{m^{3}} .

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Discussion

Her density is less than the fluid density. We expect this because she floats. Body density is one indicator of a person’s percent body fat, of interest in medical diagnostics and athletic training. (See Figure 11.23.)