In this video I go over another example on determining the amount of work done in moving an object using integrals and this time I look at pulling a rope from the top of a building. In this example, the force required to pull the rope up is not given but we can determine the force and hence the work by breaking the rope into many small pieces and then use integration to determine the equation and hence amount of work required to pull up the rope. The reason we need to consider the rope as many small pieces is because as the rope is pulled up the length of the rope changes and thus the amount of force required keeps decreasing as the length of rope being pulled up decreases.

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Integrals and Work: Example 3

Example:

A 200-lb cable is 100 ft long and hangs vertically from the top of tall building. How much work is required to lift the cable to the top of the building?

Solution: