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,

Density of the chain = Length of the chain = L = 60 mAcceleration due to gravity = g = 9.81

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)

mass of the block connected to the chain = m = 35 kg

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

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.

What are you trying to ask?