Explanation Given information: The applied force function for the spring is F ( x ) = 10 ( e 0.2 x − 1 ) . The applied force is said to be progressive if F ' ( x ) increases a x increases and is degressive if F ' ( x ) decreases a x increases. Formula used: The work done in compressing or decompressing a spring from an initial position a to final position b , when the applied force is F ( x ) , is given by the formula: Work done = ∫ a b F ( x ) d x Calculation: Consider that the applied force is F ( x ) = 10 ( e 0.2 x − 1 ) . Compute the first derivative of the function F ( x ) with respect to x as given below, F ( x ) = 10 ( e 0.2 x − 1 ) d d x ( F ( x ) ) = d d x ( 10 ( e 0.2 x − 1 ) ) F ' ( x ) = 10 × d d x ( e 0.2 x − 1 ) = 10 × ( 0.2 e 0.2 x ) { ∵ d d x ( e x ) = e x } = 2 e 0

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 6.5, Problem 10E

To determine

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The work done in stretching the spring from 6 to 12 cm and also determine whether the force is progressive of degressive.

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Chapter 6.5, Problem 9E

Chapter 6.5, Problem 11E

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Chapter 6 Solutions

Calculus: Early Transcendentals

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Tocalculate: The work done in stretching the spring from 6 to 12 cm and also determine whether the force is progressive of degressive.

Solution Summary: The author calculates the applied force function for the spring from 6 to 12 cm and determines whether the force is progressive or degressive.