Question

The human heart is a powerful and extremely reliable pump. Each day it takes in and discharges about 7500 L of blood. Assume that the work done by the heart is equal to the work required to lift this amount of blood a height equal to that of the average American female (1.63 m). The density (mass per unit volume) of blood is 1.05×103kg/m3.

Answer 1

The answers are:

a)
`Work=125,923.61J`

b)
`Power=1.46watt`

Why?

It seems that you forgot to write the questions of the problem, however, in order to help you, I will try to complete it.

The questions are:

a) How much work does the heart do in a day?

b) What is its power output in watts?

So, solving we have:

We need to convert from liter to cubic meters in order to use the given information, so:

`1L=0.001m^(3)\\\\7500L*(0.001m^(3) )/(1L)=7.5m^(3)`

Also, we need to find the mass given the density of the blood.

`1050}(kg)/(m^(3))*7.5m^(3)=7875kg`

Now, calculating how much work does the heart do in a day, we have:

`Work=Fd=mgh\\\\Work=7875kg*9.81(m)/(s^(2))*1.63m=125,923.61J`

Then, calculating what is the power output and its horsepower, we have:

`Power=(Work)/(time)\\\\Power=(125,923.61J)/(86,400s)=1.46watt`

Have a nice day!