?Show how to approximate the required work by a Riemann sum. Then express the work as an

Chapter 5, Problem 15

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QUESTION:

Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it.

A cable that weighs \(2 \quad  lb/ft\) is used to lift \(800 lb\) of coal up a mine shaft \(500 ft\) deep. Find the work done.

Equation Transcription:

Text Transcription:

2 lb/ft

800 lb

500 ft

Questions & Answers

QUESTION:

Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it.

A cable that weighs \(2 \quad  lb/ft\) is used to lift \(800 lb\) of coal up a mine shaft \(500 ft\) deep. Find the work done.

Equation Transcription:

Text Transcription:

2 lb/ft

800 lb

500 ft

ANSWER:

Step 1 of 3

Let work done on the cable be

We will divide the cable into segments, let  be the distance from the top of the mine shaft to the segment and let  be length of the segment.

Work Done on a segment  Weight of the segment  Vertical distance traveled Work Done on a segment

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