A 60-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 6 kg/m. Use 9.8 m/s 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 40-kg block is attached to the end of the chain? a. Set up the integral that gives the work required to wind the entire chain onto the cylinder using the winch. Use increasing limits of integration. 60 0 6(9.8)(60-y)) dy (Type exact answers.) The amount of work required is 105840 J. (Type an integer or a decimal.) b. Set up the integral that gives the work required to wind the chain onto the cylinder if a 40-kg block is attached to the end of the chain. Use increasing limits of integration. 60 (ugy+40y dy 0 (Type exact answers.)