In Example 3, find the work done in winding up all the cable.

EXAMPLE 3 Work done winding up cable

Find the work done in winding up 60.0 ft of a 100-ft cable that weighs 4.00 Ib/ft See

Fig. 26.65.

First, we let x denote the length of cable that has been wound up at any time.

Then the force required to raise the remaining cable equals the weight of the cable

that has not yet been wound up. This weight is the product of the unwound cable

length, 100 -x and its weight per unit length, 4.00 lb/ft or

Since 60.0 ft of cable are to be wound up, a = 0 (none is initially wound up) and b = 60.0 ft The work done is