E. coli bacteria swim by means of flagella that rotate about...

E. coli bacteria swim by means of flagella that rotate about 100 so times per second. A typical $E .$ coli bacterium swims at $22 \mu \mathrm{m} / \mathrm{s}$ its flagella exerting a force of $0.57 \mathrm{pN}$ to overcome the resistance due to its liquid environment. (a) What's the bacterium's power output? (b) How much work would it do in traversing the $25-\mathrm{mm}$ width of a microscope slide?

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Key Concepts

Unit Conversion

Unit conversion is essential for solving physics problems accurately, especially when dealing with extremely small or large values. Converting units such as micrometers to meters or picoNewtons to Newtons ensures that the calculations conform to standard SI units, making the analysis consistent and accurate.

Force

Force is an interaction that, when exerted, can cause an object to accelerate. In this context, it is used to overcome resistive forces in a fluid, enabling the motion of the bacterium. The magnitude and direction of force are crucial in determining the work done and power required for movement.

Work

Work is the measure of the energy transferred when a force is applied to an object causing displacement. It is computed as the product of the force and the displacement along the line of action of the force.

Power

Power is defined as the rate at which work is done or energy is transferred over time. In mechanical systems, it can be calculated by multiplying the force exerted on an object by the velocity at which the object moves in the direction of the force.

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