Explanation Work is defined as the amount of energy needed to perform any physical task. If constant force is applied, then the work is simply given by the following equation W = F × d Where W = W o r k d o n e F = C o n s t a n t F o r c e d = d i s t a n c e t h r o u g h w h i c h t h e f o r c e a c t s If the force applied is not constant and changes over time, then integral equation is used to calculate the work done. W = ∫ x = a x = b f ( x ) d x Where, W = W o r k d o n e f ( x ) = f o r c e a s a f u n c t i o n o f d i s t a n c e x = d i s t a n c e t h r o u g h w h i c h t h e f o r c e a c t s Given: Given a material of variable density f ( y ) = 1000 – 100 y k g / m 3 out of which a box of height 3 m and a square base of side 2 m is needed to be built. Formula Used: We know that force or weight is given as F = m a or F = m g , where is acceleration due to gravity. Also, Mass, m = V D , where V is the volume of the object and d is the density...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.5, Problem 16E

To determine

The work done against the gravity to build a box of height $3 m$ and a square base of side $2 m$ out of a material of variable density. The density of material at height $y$ is $f (y) = 1000 - 100 y k g / m^{3}$

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Chapter 6.5, Problem 15E

Chapter 6.5, Problem 17E

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Chapter 6 Solutions

Calculus - Standalone book

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The work done against the gravity to build a box of height 3 m and a square base of side 2 m out of a material of variable density. The density of material at height y is f ( y ) = 1000 – 100 y k g / m 3

Solution Summary: The author explains that work is defined as the amount of energy needed to perform any physical task. If the force applied is not constant, then integral equation is used to calculate the work done.

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The work done against the gravity to build a box of height $3 m$ and a square base of side $2 m$ out of a material of variable density. The density of material at height $y$ is $f (y) = 1000 - 100 y k g / m^{3}$

Want to see the full answer?

Chapter 6 Solutions

The work done against the gravity to build a box of height 3 m and a square base of side 2 m out of a material of variable density. The density of material at height y is f ( y ) = 1000 – 100 y k g / m 3

Solution Summary: The author explains that work is defined as the amount of energy needed to perform any physical task. If the force applied is not constant, then integral equation is used to calculate the work done.

Videos

The work done against the gravity to build a box of height 3 m and a square base of side 2 m out of a material of variable density. The density of material at height y is f(y) = 1000 – 100y kg/m3

Want to see the full answer?

Chapter 6 Solutions

The work done against the gravity to build a box of height $3 m$ and a square base of side $2 m$ out of a material of variable density. The density of material at height $y$ is $f (y) = 1000 - 100 y k g / m^{3}$