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The human heart is a powerful and extremely reliable pump. Each day it takes in and discharges about 7300 L of blood. Assume that the work done by the heart is equal to the work required to lift that amount of blood a height equal to that of the average citizen of Atlantic Falls, approximately 1.6 m. The density of blood is 1050 kg/m3. What is the heart's power output in watts?

Respuesta :

skyluke89

Answer:

1.39 W

Explanation:

The volume of blood is

[tex]V=7300 L = 7.3 m^3[/tex]

the density is

[tex]\rho = 1050 kg/m^3[/tex]

So the total mass of blood lifted in one day is

[tex]m=\rho V=(1050 kg/m^3)(7.3 m^3)=7665 kg[/tex]

So the total work done is:

[tex]W=mgh=(7665 kg)(9.8 m/s^2)(1.6 m)=1.2\cdot 10^5 J[/tex]

The total time taken is one day, so

[tex]t=24 h = 86400 s[/tex]

So the power output is

[tex]P=\frac{W}{t}=\frac{1.2\cdot 10^5 J}{86400 s}=1.39 W[/tex]

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