The human heart is a powerful and extremely reliable pump....

The human heart is a powerful and extremely reliable pump. Each day it takes in and discharges about $7500 \mathrm{~L}$ 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 Australian woman $(1.65 \mathrm{~m})$. The density (mass per unit volume) of blood is $1.05 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. (a) How much work does the heart do in a day? (b) What is the heart's power output?

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Key Concepts

Work

Work is defined as the product of force and displacement in the direction of the force. In problems involving lifting, work is calculated as the gravitational potential energy, which is the energy required to raise a mass against the force of gravity.

Gravitational Potential Energy

Gravitational potential energy quantifies the work necessary to lift an object to a certain height against gravity. It is calculated using the equation U = m × g × h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.

Density

Density is a measure of mass per unit volume and is key when converting a given volume of a substance into its corresponding mass. This concept allows us to determine the mass of a fluid like blood when its volume and density are known.

Power

Power is defined as the rate at which work is done or energy is transferred. It is calculated by dividing the total work done by the time interval over which the work is performed, providing an average power output over that period.

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