Explanation Work is referred to as the amount of energy that is required to perform any substantial 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 3 m chain having the variable mass density of ρ ( x ) = 2 x ( 4 - x ) k g / m Formula Used: The amount of work done in lifting a body to a height is given by the formula W o r k D o n e = m × g × h Where, m = mass of the object in kilograms g = acceleration due to gravity ( at the surface of the earth) h = height in meters Calculation: Let us consider a small segment of the chain of the length Δ x located at distance of meters from top end of the building. Thus, the work needed to lift the Δ x segment of chain to the top of the building is given as W j ≈ ( ρ ( x ) Δ x ) ( 9.8 ) x j J W j ≈ 39.2 Δ x x j J Now, summing over all the segments of the chain and passing to the limit Δ x → 0 , we get the total work as W o r k R e q u i r e d = ∫ 0 3 9.8 ρ ( x ) x d x W o r k R e q u i r e d = ∫ 0 3 9.8 ( 2 x ( 4 - x ) ) x d x W o r k R e q u i r e d = 9 .8 ∫ 0 3 8 x 2 - 2 x 3 d x W o r k R e q u i r e d = 9...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6.5, Problem 34E

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The work done in lifting a $3 m$ chain having the variable mass density of $ρ (x) = 2 x (4 - x) k g / m$ from its front end such that the bottom end of the chain is $2 m$ above the ground

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Chapter 6.5, Problem 33E

Chapter 6.5, Problem 35E

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The work done in lifting a 3 m chain having the variable mass density of ρ ( x ) = 2 x ( 4 - x ) k g / m from its front end such that the bottom end of the chain is 2 m above the ground

Solution Summary: The author explains that the amount of work done in lifting a 3 m chain is 661.5 J o u l e s. If the force applied is not constant and changes over time, then integral equation

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The work done in lifting a $3 m$ chain having the variable mass density of $ρ (x) = 2 x (4 - x) k g / m$ from its front end such that the bottom end of the chain is $2 m$ above the ground

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Chapter 6 Solutions

The work done in lifting a 3 m chain having the variable mass density of ρ ( x ) = 2 x ( 4 - x ) k g / m from its front end such that the bottom end of the chain is 2 m above the ground

Solution Summary: The author explains that the amount of work done in lifting a 3 m chain is 661.5 J o u l e s. If the force applied is not constant and changes over time, then integral equation

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The work done in lifting a 3 m chain having the variable mass density of ρ(x) = 2x(4 - x) kg/m from its front end such that the bottom end of the chain is 2 m above the ground

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Chapter 6 Solutions

The work done in lifting a $3 m$ chain having the variable mass density of $ρ (x) = 2 x (4 - x) k g / m$ from its front end such that the bottom end of the chain is $2 m$ above the ground