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Work & Energy of a hanging rope

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A rope having a total mass of 0.4kg and total length 4m has 0.6m of the rope hanging vertically down off a work bench. How much work must be done to place all the rope on the bench?

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Step by step solution provided for how much work must be done to place all the ropes on the bench.

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The fig. shows 3.4 m of the rope on the bench and 0.6 m hanging down.
Total mass of the rope = 0.4 kg
Mass per unit length = 0.4/4 = 0.1 kg/m
Force on the rope is on account of the weight of its hanging portion.
Hence, initial force acting on the rope (trying to pull it down from the bench) = Mass of the hanging portion x g = Length of the hanging portion x Mass per unit length x g = 0.6 x ...

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