A 3.0 m long steel chain is stretched out along the top level of a horizontal sc

Question

A 3.0 m long steel chain is stretched out along the top level of a horizontal scaffold at a construction site, in such a way that x = 1.9 m of the chain remains on the top level and y = 1.1 m hangs vertically. (See the figure.) At this point, the force on the hanging segment is sufficient to pull the entire chain over the edge. Once the chain is moving, the kinetic friction is so small that it can be neglected. How much work is performed on the chain by the force of gravity as the chain falls from the point where 1.9 m remains on the scaffold to the point where the entire chain has left the scaffold?

Explanation / Answer

Work done by gravity = work done on c.o.m
Initial centre of y part of chain = 0.55 m below the table
Initial com of x part = 0 m above the table
Initial P.E. [considering p.e. at table = 0] = -mgh = -(1.1mg*0.55/3) = -1.9763 m
Final P.E. = mg(-1.5) = -14.7 m

Work done on chain by gravity = 12.724 m J [where m is mass of the chain]

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