A60-m-long chain hangs vertically from a cylinder attached to a winch. assume there is no friction in the system and that the chain has a density of 10 kg/m. use 9.8 m divided by s squared for the acceleration due to gravity. a. how much work is required to wind the entire chain onto the cylinder using the winch? b. how much work is required to wind the chain onto the cylinder if a 35-kg block is attached to the end of the chain?

part (a). 176580 J

part (b). 197381 J

Explanation:

Given,

part (a)

Let dy be the small element of the chain at a distance of 'y' from the ground.

mass of the small element of the chain =

Work done due to the small element,

Total work done to wind the entire chain = w

part (b)

Total work done to wind the chain = work done due to the chain + work done due to the mass

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