Concept explainers
To Calculate: The work done to lift a load of coal from a mine shaft using a heavy cable.
Answer to Problem 13E
Explanation of Solution
Given Information: The cable weighs
Concept Used: The work done by a force
If the force is constant, then work done can be expressed as
Calculate the work done on the cable and the work done on the load of coal separately and then add them
Work done on shaft:
The weight of an infinitesimally short element of the cable with length
Work required to pull this infinitesimally small element to the ground is
The work required to pull the entire cable to the top of the building is the integral of
Work done on coal: Multiply the weight of the coal (force) with the depth of the coal (displacement) to get the work done on the coal to write
So, the total work done is
Chapter 6 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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