A 9m long chain with a mass of 54kg is hanging from the ceiling of a warehouse and a hook is attached to it 3m from its bottom end. Compute the work done to pull the hook (with the chain attached to it!) to the ceiling, so that the chain will be folded into three equal sections.

Question

anonymous · Answer

mass of 1m length equal to 54/9=6kg.
first  of all we calculate the initial potential energy of the when it is straight .
Ui=mg(h/2)because the centre of mass of the chain in the middle.hence we take h/2.where h is the total length of the string.here h=9m and m=54 kg.
at the final position its potential energy will be
Uf=m1g(h1/2)(for first section)+m1g(h2)(for second section)+m1g(h1/2)(for third section)
   where m1=((9-3)/3)*6kg=12kg
            h1=(9-1)=8m
          and h2=(9-2)=7m
we know that total workdone=change in potential energy =Uf-Ui....calculate it and get your answer....