An elevator at the bottom of a 80 foot shaft weighs 1500 pounds. The 80 foot...

An elevator at the bottom of a 80 foot shaft weighs 1500 pounds. The 80 foot cable that lifts the elevator weighs 400 pounds. Assume that the cable has uniform weight over its length. Answer the following questions to calculate the work that is done to raise the elevator 50 feet up from the bottom of the shaft. (a) Write a Riemann sum that approximates the work needed to lift the 50 ft up the shaft. (b) Write and evaluare an integral to calculate the work done to raise the cable 50 ft up the shaft. (c) What is the total work required to lift the cable and elvator 50 ft up the shaft?

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