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Question Number 21731 by Tinkutara last updated on 02/Oct/17

A very flexible uniform chain of mass M  and length L is suspended vertically so  that its lower end just touches the  surface of a table. When the upper end  of the chain is released, it falls with  each link coming to rest the instant it  strikes the table. Find the force exerted  by the chain on the table at the moment  when x part of chain has already rested  on the table.

$$\mathrm{A}\:\mathrm{very}\:\mathrm{flexible}\:\mathrm{uniform}\:\mathrm{chain}\:\mathrm{of}\:\mathrm{mass}\:{M} \\ $$$$\mathrm{and}\:\mathrm{length}\:{L}\:\mathrm{is}\:\mathrm{suspended}\:\mathrm{vertically}\:\mathrm{so} \\ $$$$\mathrm{that}\:\mathrm{its}\:\mathrm{lower}\:\mathrm{end}\:\mathrm{just}\:\mathrm{touches}\:\mathrm{the} \\ $$$$\mathrm{surface}\:\mathrm{of}\:\mathrm{a}\:\mathrm{table}.\:\mathrm{When}\:\mathrm{the}\:\mathrm{upper}\:\mathrm{end} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{chain}\:\mathrm{is}\:\mathrm{released},\:\mathrm{it}\:\mathrm{falls}\:\mathrm{with} \\ $$$$\mathrm{each}\:\mathrm{link}\:\mathrm{coming}\:\mathrm{to}\:\mathrm{rest}\:\mathrm{the}\:\mathrm{instant}\:\mathrm{it} \\ $$$$\mathrm{strikes}\:\mathrm{the}\:\mathrm{table}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{force}\:\mathrm{exerted} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{chain}\:\mathrm{on}\:\mathrm{the}\:\mathrm{table}\:\mathrm{at}\:\mathrm{the}\:\mathrm{moment} \\ $$$$\mathrm{when}\:\mathrm{x}\:\mathrm{part}\:\mathrm{of}\:\mathrm{chain}\:\mathrm{has}\:\mathrm{already}\:\mathrm{rested} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{table}. \\ $$

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