Physics

Consider the center of mass of the part of the chain that is initially hanging:

The mass of the part of the chain that is initially hanging is (since the mass is uniformly distributed).

The center of mass of this part is at a distance from the table edge.

 

Calculate the initial potential energy of the hanging part:

The initial gravitational potential energy of the hanging part (negative because it is below the table level which we can take as the reference point for potential energy, ).

 

Substituting , we get

 

Calculate the final potential energy of the chain when it is completely hanging:

When the chain is completely hanging, the center of mass of the whole chain is at a distance below the table level.

The mass of the whole chain is .

The final gravitational potential energy (negative because it is below the reference point).

 

Calculate the work done by gravity:

the work done by gravity is equal to the change in gravitational potential energy, but with the opposite sign,