A uniform chain of length L and mass M overhangs a horizontal table with two-thirds of its length on the table. The friction coefficient between chain and table is µ. Find the work done by friction while the chain slips completely off the table.
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Question

A uniform chain of length L and mass M overhangs a horizontal table with two-thirds of its length on the table. The friction coefficient between chain and table is µ. Find the work done by friction while the chain slips completely off the table.

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G1 Physics · Accepted Answer

As the chain slides, the length remaining on the table decreases continuously. Integrating friction f=µ(λx)g over the displacement until the chain leaves the table gives W(f)=-(2/9)µMgL.