Final answer:
The work done to lift a hanging part of a uniform cable is calculated as the product of the force, which is the weight of the part being lifted (mg), and the distance it is lifted, with the formula W = mgh.
Step-by-step explanation:
To calculate the work done in lifting a uniform cable of mass m and length l hanging over the side of a surface, you consider the force required and the distance over which the force is applied. The force needed is equal to the weight of the part of the cable that is hanging, which is mg, where g is the acceleration due to gravity. To lift this hanging part up to the surface at constant speed, the distance you'd lift it is equal to the length of the cable that is hanging over the edge.
Assuming no friction or other resistive forces, the work done on the cable (W) is the product of the force applied (F) and the distance (d) through which the force is applied. Therefore, if a length h of the cable is hanging over the edge, the work done W to lift it is W = mgh, where h is the length of the cable that is hanging and being lifted up.
In more complex scenarios, such as using a pulley system with mechanical advantage (MA), the work done could be distributed differently due to the pulleys. However, without a pulley system, the direct application of force to the weight of the cable is calculated simply as mgh.