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A force $\vec{F}$ in the positive direction of an $x$ axis acts on an object moving along the axis. If the magnitude of the force is $F=10 e^{-x / 2.0}$$N,$ with $x$ in meters, find the work done by $\vec{F}$ as the object moves $\mathrm{N},$ with $x$ in meters, find the work done by $\vec{F}$ as the object movesfrom $x=0$ to $x=2.0 \mathrm{m}$ by (a) plotting $F(x)$ and estimating the areaunder the curve and (b) integrating to find the work analytically.

(a) 14 $\mathrm{J}$(b) $-12.6 \mathrm{J}$

Physics 101 Mechanics

Chapter 7

Kinetic Energy and Work

Work

Kinetic Energy

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

Lectures

04:16

In mathematics, a proof is…

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As an object moves along t…

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The force on a particle is…

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As a particle moves along …

06:09

A force $F(x)=(3.0 / x) \m…

01:30

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02:43

A force $\vec{F}$ acts in …

04:37

A force $\overrightarrow{\…

02:00

A particle of mass $2.0 \m…

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The force acting on a part…

but a off the given problem The plot moved off. The function function will be following. You have here X axis, which is X displacement. And here's the force, which is function off X. This is a maximum 10 euros. Zero. And here is to, uh yeah, 0.2 divisions Airport, four divisions. And here is the one. Um, this is a 24 mmm 68 since a 10. So the plot off the function will be following the cream's is here and up to do two year estimating the area under the curve Allow lust for the range off the answers. Ah, from from 11 Joel to our 14. Jules, if you're looking, uh, this plot, the work will be called to simply the 80 under this curve, which is a force times, displacement, X, but be we can estimate the area analytically by taking integration from 0 to 2 max exes were given function that is staying. He excellent, too. DX We integrate this, we get the minus 20 e minus X divided too. The limits for the X 0 to 2. So this gives us ah, 12.6 jewels, which is approximately 13. Jules

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