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Work from force How much work is required to move an object from $x=1$ to $x=3$ (measured in meters) in the presence of a force (in $\mathrm{N}$ ) given by $F(x)=\frac{2}{x^{2}}$ acting along the $x$ -axis?

Name: Problem 22, Chapter 6: Calculus: Early Transcendentals
Uploaded: 2020-06-19T18:55:15-08:00
Duration: 2 min 49 s
Channel: Samuel Coplin
Description: Work from force How much work is required to move an object from x=1 to x=3 (measured in meters) in the presence of a force (in N ) given by F(x)=(2)/(x^2) acting along the x -axis?

   Work from force How much work is required to move an object from $x=1$ to $x=3$ (measured in meters) in the presence of a force (in $\mathrm{N}$ ) given by $F(x)=\frac{2}{x^{2}}$ acting along the $x$ -axis?

Calculus: Early Transcendentals

William Briggs, Lyle… 3rd Edition

Chapter 6, Problem 22

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Solved by Expert Samuel Coplin

06/19/2020

Step 1

The work done by a variable force is given by the integral of the force over the distance. So, we need to evaluate the integral $\int_{1}^{3} F(x) dx$. Show more…

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Work from force How much work is required to move an object from $x=1$ to $x=3$ (measured in meters) in the presence of a force (in $\mathrm{N}$ ) given by $F(x)=\frac{2}{x^{2}}$ acting along the $x$ -axis?

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Key Concepts

Work as the Integral of Force

Work is defined as the accumulation of energy along a path when a force is applied. In cases where the force varies with position, work is calculated by integrating the force function with respect to displacement over the specified interval.

Definite Integral

The definite integral is a fundamental concept in calculus used to compute the total accumulation of a quantity, like work, over a specific interval. It provides a way to sum infinitesimal contributions along a path, making it vital for calculations involving variable forces.

Variable Force

A variable force is one that changes in magnitude and possibly direction over the distance it acts. Understanding and representing force as a function of position is essential in accurately computing work when the applied force is not constant.

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