Chapter 5.4, Problem 19E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

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

A 10-ft chain weighs 25 lb and hangs from a ceiling. Find the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end.

To determine

**To find:**

Work done in lifting the lower end of the chain to the ceiling

Explanation

**1) Concept:**

Approximate the required work by using the concept of Riemann sum. Then express the work as an integral and evaluate it.

**2) Given:**

i) Weight of the chain

ii) Length of the chain

**3) Calculation:**

Letâ€™s place the origin at the top of the ceiling and

If

Total Length of chain

The length of chain per foot is

The weight of the

Divide the length of chain

The upper part of the chain is

To find the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end.

The lower part of the chain is

Distance of point

When lifting the point

Therefore,

The lower part of the chain ( for

The work needed to lift for the

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