Chapter 5.4, Problem 16E

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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 chain lying on the ground is 10 m long and its mass is 80 kg. How much work is required to raise one end of the chain to a height of 6 m?

To determine

**To find:**

Work required to raise one end of the chain to a height of

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:**

Length of chain

Mass of chain

**3) Definition 4:**

**4) Calculation:**

Chain lying on the ground is

Out of the

Total length of the chain if one end of the chain is raised to a height of

Total mass of chain

Total length of chain

Mass per unit length of chain is

The force acting on the chain is

Where

Force per unit length acting on the chain is

The work done acting on the chain is

Where

To find the work required to raise one end of the chain to a height of

Use an argument similar to the one that leads to Definition

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