Physics

To calculate the gravitational potential energy (GPE) of the chain, we need to consider the center of mass of the portion of the chain that is hanging off the edge of the table and the portion that is on the table.

 

The chain has a total length and mass .

Half of the chain is hanging off the edge of the table, so the length of the hanging part is , and the other half is resting on the table.

 

Gravitational potential energy of the hanging part

For the hanging part of the chain:

The mass of the hanging part is proportional to its length, so the mass of the hanging section is .

The center of mass of the hanging part is at the midpoint of its length, which is at a height of (since the hanging part starts from the edge of the table).

 

The gravitational potential energy for the hanging part is:

Click "Show Answer" to reveal the answer and analysis