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 chain of 3 m having the variable mass density of ρ ( x ) = x 2 – 3 x + 10 k g / m for 0 ≤ x ≤ 3 . 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...

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6.5, Problem 33E

To determine

The work done in lifting a $3 m$ chain over the side of a building if the chain has the variable mass density of $ρ (x) = x^{2} - 3 x + 10 k g / m$ for $0 \leq x \leq 3$

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Chapter 6.5, Problem 32E

Chapter 6.5, Problem 34E

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Chapter 6 Solutions

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The work done in lifting a 3 m chain over the side of a building if the chain has the variable mass density of ρ ( x ) = x 2 – 3 x + 10 k g / m for 0 ≤ x ≤ 3

Solution Summary: The author explains that work is the amount of energy required to perform any substantial task. If the force applied is not constant and changes over time, then integral equation is used to calculate the work done.

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The work done in lifting a $3 m$ chain over the side of a building if the chain has the variable mass density of $ρ (x) = x^{2} - 3 x + 10 k g / m$ for $0 \leq x \leq 3$

Want to see the full answer?

Chapter 6 Solutions

The work done in lifting a 3 m chain over the side of a building if the chain has the variable mass density of ρ ( x ) = x 2 – 3 x + 10 k g / m for 0 ≤ x ≤ 3

Solution Summary: The author explains that work is the amount of energy required to perform any substantial task. If the force applied is not constant and changes over time, then integral equation is used to calculate the work done.

Videos

The work done in lifting a 3 m chain over the side of a building if the chain has the variable mass density of ρ(x) = x2 – 3x + 10 kg/m for 0 ≤ x ≤ 3

Want to see the full answer?

Chapter 6 Solutions

The work done in lifting a $3 m$ chain over the side of a building if the chain has the variable mass density of $ρ (x) = x^{2} - 3 x + 10 k g / m$ for $0 \leq x \leq 3$