## Monday, December 21, 2015

### Work done in pulling the suspended chain back on to the table

If a portion of chain is hanging from the edge of the table, to pull it back on to the table, we need to do some work. Let us consider a chain of mass m and length l is available for you. Let a portion of chain is hanging on the table which is a part of total chain. Being chain is a one dimensional body; mass of the chain is directly proportional to the length of the chain.

We can measure the mass of the hanging part of the chain by multiplying the linear density of the chain with the portion of the chain hanging. Linear density is the mass of the chain for unit length.

We would like to pull the portion of the chain back on to the table, we need to do some work done and here we would like to measure the work done. The hanging portion of the chain is having distributed mass and it cannot be treated as a point mass. We shall consider a point where the mass is concentrated in the suspended portion of the body and it is called center of mass. For a regular body, it is at the geometrical center itself.

We need to do the work to pull back the suspended part back on to the table and it is equal to the potential energy of the suspended portion of the chain.

A detailed video lesson is made here and a model problem is also done by assuming that one third of the chain is hanging.

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