According to a simplified model of a mammalian heart, at each pulse, approximately 20 ml of blood is accelerated from 0.26 m/s to 0.36 m/s during a period of 0.08 seconds. How do you find the...

According to a simplified model of a mammalian heart, at each pulse, approximately 20 ml of blood is accelerated from 0.26 m/s to 0.36 m/s during a period of 0.08 seconds. How do you find the magnitude of the force exerted by the heart muscle? 

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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The magnitude of the force exerted by the heart muscle can be calculated by using the Newton's Second Law of Motion, that is, force exerted is the product of mass times the acceleration. Here, blood is accelerated from 0.26 m/s to 0.36 m/s in a span of 0.08 seconds. Thus, the acceleration of blood can be calculated as the rate of change of velocity, or

Acceleration of blood =  dv/dt = (0.36 - 0.26)/0.08 m/s^2 = 1.25 m/s^2

The volume of blood accelerated = 20 ml.

The density of blood = 1060 gm/lt or, 1.060 gm/ml

Thus, the mass of blood = volume x density = 20 ml x 1.060 gm/ml = 21.2 gm = 0.0212 kg

Therefore, the force exerted by the heart muscle = mass x acceleration

= 0.0212 kg x 1.25 m/s^2  = 0.0265 N

Hope this helps.

 

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