During each heartbeat, about 80 g of blood is pumped into the aorta in approximately 0.2 s....

Question:

During each heartbeat, about 80 g of blood is pumped into the aorta in approximately 0.2 s. During this time, the blood is accelerated from rest to about 1 m/s.

A) How much work is done by the heart on the blood during this time?

0.08 J

0.04 J

0.4 J

40 J

B).If the heart beats 60 times in 1 minute, how much blood moves through the heart in 10 hours?

48 kg

288,000 kg

14,400 kg

2880 kg

C).What is the power output of the heart needed to perform one heartbeat?

2 W

0.4 W

200 W

0.2 W

Work and Power

One way to find the work done on an object is to determine its change in energy. In this problem, the heart does work on the blood to accelerate it. When the blood accelerates, it increases its kinetic energy. We know the initial kinetic energy = 0 and we can find the final kinetic energy using:

{eq}KE= 1/2*m*v^2 {/eq}

If we use kg for mass and m/s for velocity, we should get our work in Joules.

To determine the power, we need to consider the equation:{eq}P=W/t {/eq}

If we know the amount of work done and the time this took, we can determine the power. If we use the units of Joules for seconds for time, our power will be measured in Watts.

To solve for the amount of blood that flows, we need to consider the rate at which the heart beats and the time we are considering. Using these values and some dimensional analysis, we can easily determine the amount of blood that is moved during this time interval.

Answer and Explanation:

a) Initial KE = 0 Final KE:

{eq}KE_f=1/2*0.080*1^2= ).04J {/eq}

So the work done is 0.04J

b) Each time the heart beats, it moves 80 g of blood. It beats 60 times in a minute or 1 time every second.

10 hours is 36000 seconds. So the heart would move 2880000g of blood in 10 hours. Converting to Kg = 2880 kg

c). Power for 1 heart beat . Using the equation for power above:

{eq}P=0.04J/.2s = .2 Watts {/eq}


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