$\"\"$

\

A $\"\"$ pound ball is suspended from a demolition crane from a $\"\"$ foot cable.

\

Cable weighs $\"\"$ pounds per foot.

\

Let the cable is divided into small sections each of length $\"\"$ .

\

Total weight of the chain and ball is $\"\"$ pounds.

\

The weight of each section is increment of the force.

\

$\"\"$

\

Suppose that the ball is raised to a height of $\"\"$ units.

\

The increment of work is $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

(a)

\

Find the work required to wind up $\"\"$ feet of the apparatus.

\

Here $\"\"$ ranges from $\"\"$ to $\"\"$ .

\

$\"\"$

\

Work required to wind up $\"\"$ feet of the apparatus is $\"\"$ foot pounds.

\

$\"\"$

\

(b)

\

Find the work required to wind up all $\"\"$ feet of the apparatus.

\

Here $\"\"$ ranges from $\"\"$ to $\"\"$ .

\

$\"\"$

\

Work required to wind up $\"\"$ feet of the apparatus is $\"\"$ foot pounds.

\

$\"\"$

\

(a) Work required to wind up $\"\"$ feet of the apparatus is $\"\"$ foot pounds.

\

(b) Work required to wind up $\"\"$ feet of the apparatus is $\"\"$ foot pounds.