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What amount of force must the flagellum generate to propel the bacterium at a constant velocity of 0.003 $\mathrm{m} / \mathrm{s} ?$A. $1.5 \times 10^{-10} \mathrm{N}$B. $5 \times 10^{-10} \mathrm{N}$C. $9 \times 10^{-7} \mathrm{N}$D. $1.8 \times 10^{-7} \mathrm{N}$

see solution.

Physics 101 Mechanics

Chapter 4

Newton's Laws of Motion

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Simon Fraser University

University of Sheffield

University of Winnipeg

McMaster University

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

01:46

If the bacterium wished to…

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necked for the bacterium to travel are constant velocity, constant velocity. We need nan acceleration of zero known accelerations. This means obviously that net forces on the material are also zero. So all we need to do here is compute the force exerted by the bacterial itself and that we're equal the force exerted by the flash and for forcing your ex elevation for acceleration returned to this equation Emotion. He squared because V not squared. Plus two times eight tons distance. You're not his initial velocity and some introduces too. And so this can be written as a equals B squared minus. You not squared over two X and so they're given. But V equals point. 003 meters per second. And then we're given that X are rather side ivy. Not because the initial speed will be that. And you wanted to come to rest and then Vienna on then X is 10 to the negative to Nana leaders remember, our Nano has 10 to the negative nine. So this is 10 to the negative. 11 meters. Okay? Therefore you have that acceleration is negative. So this goes where Negative point, though 03 meters per seconds. square over two times 10 to the negative 11 meters. This comes out to negative 4.5 times 10 to the, uh 10 to the five meters per second squared. And you will have found this. If you're deaf, you work through problems 58 and so of the final step here is just Newton's second law affray calls mass times acceleration and so mass is given as 10 to the negative 12 grams. And again, we have a unit conversion issue here. Certainly, native Grams, remember, Graham is 1,000 of a kilogram. So you divide that by 1,000 to get 10 to the negative 12 over 1,000 kilograms times this acceleration you just found, um and so this gives you negative 4.5 tons. 10 to the negative 10. Newton's time course. And so the correct answer, therefore, is me. Negative. Five times 10 to the negative. 10. Uh, this is just from rounding this off. It's number off to the first significant figure, and that's what

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