# Chapter 6 - Problems - Page 231: 77

The average mechanical power output of the heart is 5.25 Watts.

#### Work Step by Step

We can find the volume of blood pumped into the aorta each second: $5.0~L/min \times \frac{1~m^3}{10^3~L} \times \frac{1~min}{60~s} = 8.33\times 10^{-5}~m^3/s$ We can find the area of the aorta: $A = \pi~r^2 = (\pi)(0.009~m)^2 = 2.54\times 10^{-4}~m^2$ We can find the speed $v$ of the blood in the aorta: $A~v = 8.33\times 10^{-5}~m^3/s$ $v = \frac{8.33\times 10^{-5}~m^3/s}{A}$ $v = \frac{8.33\times 10^{-5}~m^3/s}{2.54\times 10^{-4}~m^2}$ $v = 0.328~m/s$ We can find the heart's power output: $P = F~v = (16~N)(0.328~m/s) = 5.25~Watts$ The average mechanical power output of the heart is 5.25 Watts.

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