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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 6.6 - Problem 22e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 6.6 - Problem 22e

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# Work function A spring has a restoring force given by F(x) ISBN: 9780321570567 2

## Solution for problem 22E Chapter 6.6

Calculus: Early Transcendentals | 1st Edition

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Problem 22E

Work function A spring has a restoring force given by F(x) = 25x. Let W(x)be the work required to stretch the spring from its equilibrium position (x = 0) to a variable distance x. Graph the work function. Compare the work required to stretch the spring x units from equilibrium to the work required to compress the spring x units from equilibrium.

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Solution 22E Step1 Given that A spring has a restoring forcegiven by ( 5 . Let W )be the work required to stretch the spring from its equilibri m position = 0) to a variable distance x. Step2 To Find Graph the work function. Compare the work required to stretch the spring x units from equilibrium to the work required to compress the spring x units from equilibrium. Step3 A spring has a restoring force given by, F(x)=25x The work required to stretch the spring from its equilibrium position(x=0)to a variable distance is expressed as function of x given by W(x).. If the spring is stretched then distance is positive and on being compressed it is negative. Step4 The work is done in stretching the spring x units from its equilibrium position is b W=f(x) dx a x =25x dx 0 x =25 dx 0 x x2 =25 [ 2 0 x2 = 25[ 2 -0] x2 =25* 2 = 12.5x 2 Therefore, The work is done in stretching the spring x units from its equilibrium position is 2 12.5x -------------------(1) Step5 The work is done in compressing the spring x units from its equilibrium position is b W= (x) dx a x = 25x dx 0 x =25 x dx 0 x2 x =25 [ 2 0 x2 = 25[ 2-0] x2 =25* 2 2 = 12.5x Therefore, The work is done in compressing the spring x units from its equilibrium position is 2 12.5x -------------------(2) Step6 Graph for work function is Step7 From equations (1)and (2), we get that work done is equal and Positive for compressing or stretching the spring to a distance x

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##### ISBN: 9780321570567

The full step-by-step solution to problem: 22E from chapter: 6.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 22E from 6.6 chapter was answered, more than 325 students have viewed the full step-by-step answer. This full solution covers the following key subjects: work, spring, Equilibrium, required, function. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “Work function A spring has a restoring force given by F(x) = 25x. Let W(x)be the work required to stretch the spring from its equilibrium position (x = 0) to a variable distance x. Graph the work function. Compare the work required to stretch the spring x units from equilibrium to the work required to compress the spring x units from equilibrium.” is broken down into a number of easy to follow steps, and 62 words.

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