A chain is held on a frictionless table with (1/n)th of its length hanging over the edge. If the chain has a length L and mass M, how much work is required to pull the hanging part back on the table ?
Alternative approach (using center of mass): Let us take the tabletop as our reference level where potential energy is zero. Initially Ln length is hanging whose mass is MLLn=Mn and center of mass is L2n below the table. Initial PE=−MngL2n Finally, no length is hanging, and the center of mass is on the table. So, Final PE=0 As we know that Wext=Δ(U+K) Looking at initial and final situation, kinetic energy is zero in both cases. ∴Wext=PEf−PEi Wext=0−(−MngL2n)=MgL2n2 |