What’s the answer

Question

at a resting pulse rate of 81 beats per minute, the human heart typically pumps about 73 mL of blood per beat. Blood has denstity of 1060 kg /m³. Circulating all of the blood in the body through the heart takes about 1 min for a person at rest. 

 

a. how much blood is in the body?

b. On average, what mass of blood does the heart pump with each heart beat?

Answer 1

This looks like a dimensional analysis problem.

a. Let's use variable A to represent all the blood in the human body.

Givens:

resting pulse rate = 81 beat/min

pump volume = 73mL/beat

resting circulation rate = A /1 min

Solution:

You can get circulation rate by multiplying the pulse rate by the pump volume:

A /min = 81beat/min * 73mL/beat

Multiplying and canceling out the units, you get

A = 5913 mL of blood in the body

b. This is a simpler dimensional analysis problem:

we just need to convert the pump volume to pump mass.

density = mass/volume => mass = density * volume

mass = 1060kg/m³ * 73mL

To multiply these together, we need to convert the volume to have the same units.

1 m³ = 10⁶mL

mass = 1060kg/m³ * 73mL * 1m³ /10⁶mL

=0.007738 kg = 7.738 g