Left ventricle pumping The lower left chamber of the heart...

Left ventricle pumping The lower left chamber of the heart (the left ventricle) pumps blood into the aorta. According to biophysical studies, a left ventricular contraction lasts about 0.20 s and pumps 88 $\mathrm{g}$ of blood. This blood starts at rest and after 0.20 $\mathrm{s}$ is moving through the aorta at about 2 $\mathrm{m} / \mathrm{s}$ . (a) Estimate the force exerted on the blood by the left ventricle. $(\mathrm{b})$ What is the percent uncertainty in your answer? (c) What assumptions did you make? Did the assumptions increase or decrease the calculated value of the force compared to the actual value?

Left ventricle pumping The lower left chamber of the heart (the left ventricle) pumps blood into the aorta. According to biophysical studies, a left ventricular contraction lasts about 0.20 s and pumps 88 $\mathrm{g}$ of blood. This blood starts at rest and after 0.20 $\mathrm{s}$ is moving through the aorta at about 2 $\mathrm{m} / \mathrm{s}$ . (a) Estimate the force exerted on the blood by the left
ventricle. $(\mathrm{b})$ What is the percent uncertainty in your answer? (c) What assumptions did you make? Did the assumptions increase or decrease the calculated value of the force compared to the actual value?

Key Concepts

Uncertainty Estimation

Uncertainty estimation involves quantifying the potential errors or variability in a calculated result due to approximations and measurement limitations. Percent uncertainty provides a sense of how reliable a computed value is by comparing the magnitude of the uncertainty to the value itself. This is essential in physics to understand the precision of theoretical predictions or experimental measurements.

Modeling Assumptions

Modeling assumptions are simplifications or idealizations made to facilitate the analysis of complex physical systems. These assumptions, such as treating the acceleration as constant or ignoring friction and other dissipative forces, are critical for performing tractable calculations but can introduce discrepancies when compared to actual systems. Recognizing and evaluating these assumptions helps to estimate whether the calculated values are likely to be overestimates or underestimates of real-world values.

Impulse and Momentum

The concept of impulse relates to the change in momentum of an object when a force is applied over a certain time interval. In these problems, impulse is used to estimate the force required to bring about a given change in momentum, with the expression impulse = force × time equal to the change in momentum. This approach simplifies the analysis of forces in situations involving sudden accelerations.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the rate of change of its momentum, often expressed as F = ma. In problems like these, the acceleration of an object (or fluid mass) is deduced from the change in velocity over the time interval, and then the force is calculated by multiplying the acceleration by the mass. This principle underpins the relationship between force, mass, and acceleration in all dynamics problems.

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