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Ch 06: Dynamics I: Motion Along a Line
Chapter 6, Problem 6

An E. coli bacterium can be modeled as a sphere that has the density of water. Rotating flagella propel a bacterium through 40°C water with a force of 65 fN, where 1 fN = 1femtonewton = 10^-15 N. What is the bacterium's speed in micrometers/s?

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density and Volume

Density is defined as mass per unit volume and is crucial for understanding how the mass of the E. coli bacterium relates to its size. Since the bacterium is modeled as a sphere, its volume can be calculated using the formula V = (4/3)πr³, where r is the radius. Knowing the density allows us to determine the mass of the bacterium, which is essential for calculating its motion in a fluid.
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Force and Motion

Newton's second law states that force equals mass times acceleration (F = ma). In this scenario, the force exerted by the flagella propelling the bacterium can be used to find its acceleration. Understanding how force influences motion is key to determining the speed of the bacterium as it moves through the water.
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Speed Calculation

Speed is defined as the distance traveled per unit of time. In this context, once the acceleration of the bacterium is determined from the force and mass, we can calculate its speed. The conversion from meters per second to micrometers per second is also necessary, as the question specifically asks for the speed in micrometers/s, highlighting the importance of unit conversion in physics.
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