$\"\"$

Take the bottom of the chain and raise it to the $\"\"$ level, leaving the chain doubled and still hanging vertically.

The chain divided into small sections each of length $\"\"$ .

The chain is doubled and still hanging vertically, the distance is $\"\"$ .

The weight of the each section is the increment of force is $\"\"$ .

Initially the chain is on the ground, and it is raised to height of $\"\"$ , the increment of work is

$\"\"$ .

The length of the chain $\"\"$ ranges from $\"\"$ to $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

$\"\"$ .