Explanation Given: The length of the chain is 10 m. The mass of the chain is 80 kg. Calculation: Consider the value of acceleration due to gravity as 9.8 m/s 2 . Consider the friction between the chain and the floor is negligible. Calculate the length of the chain lies on the floor after lifting 6 m of the chain as follows: L = 10 m − 6 m = 4 m Consider the weight density of the chain is constant throughout the length. Calculate the mass of the chain per unit length as follows. m = 80 kg 10 m = 8 kg/m Divide the chain into n layers as x 1 , x 2 , x 3 ... x n . Consider a small strip of width Δ x , at a distance x i ∗ from the lifted end. Calculate the mass of the strip of width Δ x using the relation. m i = unit mass of chain×width of the strip = m × Δ x = 8 kg m × Δ x m =8 Δ x kg Calculate the work done to lift the strip of width Δ x using the relation: W i = w i d = m i g d (1) Here, w is the weight of the chain, d is the lift of the chain, m i is the mass of the strip of chain and g is the acceleration due to gravity

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ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

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Chapter 5.4, Problem 16E

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To express: The work done to raise one end of a chain to 6 m height as Riemann sum.

To calculate: the work done to raise one end of a chain to 6 m height.

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Chapter 5.4, Problem 15E

Chapter 5.4, Problem 17E

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To express: The work done to raise one end of a chain to 6 m height as Riemann sum. To calculate: the work done to raise one end of a chain to 6 m height.

Solution Summary: The author explains the work done to raise one end of a chain to 6 m height as Riemann sum.