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A varying force is given by $F = A e ^ { - k x } ,$ where $x$ is the position; $A$ and $k$ are constants that have units of $\mathrm { N }$ and $\mathrm { m } ^ { - 1 }$ , respectively. What is the work done when $x$ goes from 0.10$\mathrm { m }$ to infinity?

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$\frac{A}{k} e^{-0.10 k}$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

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In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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7.77. So we have ah, variable force that's given by this exponential here. Um X has units of meters k has units of inverse meters in a hazardous Newton's. We want to find the work that this force does going from X equals 0.1 meter to infinity. So we're assuming that the ex the force has to be in the ex direction because no other sort of information is given to us. So the angle is going to be zero between the force of the displacement. And so the work is just going to be integral of the forces Time displacement a k x x. This is negative a over K. You need to the negative k x one meters to entity. And so then this gives us a over k times he to the negative one meters times K

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