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A chain 10 feet long weighs 8 pounds per foot and is hung from a platform 35 feet above the ground. How much work (in ft-lb) is required to raise the entire chain to the 35-foot level?

A chain 10 feet long weighs 8 pounds per foot and is hung from a platform 35 feet above the ground. How much work (in ft-lb) is required to raise the entire chain to the 35-foot level?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** A chain 10 feet long weighs 8 pounds per foot and is hung from a platform 35 feet above the ground. How much work (in ft-lb) is required to raise the entire chain to the 35-foot level? **Explanation:** This problem involves calculating the work done in raising a chain vertically. The work done is typically calculated using the formula for work, which requires knowing the force applied and the distance over which the force is applied. 1. **Chain Details:** - Length: 10 feet - Weight: 8 pounds per foot 2. **Platform Height:** - 35 feet above the ground 3. **Goal:** - Raise the chain to the platform level. To solve, you need to integrate the weight of each infinitesimal section of the chain over the distance it needs to be raised. Because the chain is uniform, the solution involves setting up and solving an appropriate integral. The work done lifting each portion of the chain will vary based on its starting height off the ground.
Transcribed Image Text:**Problem Statement:** A chain 10 feet long weighs 8 pounds per foot and is hung from a platform 35 feet above the ground. How much work (in ft-lb) is required to raise the entire chain to the 35-foot level? **Explanation:** This problem involves calculating the work done in raising a chain vertically. The work done is typically calculated using the formula for work, which requires knowing the force applied and the distance over which the force is applied. 1. **Chain Details:** - Length: 10 feet - Weight: 8 pounds per foot 2. **Platform Height:** - 35 feet above the ground 3. **Goal:** - Raise the chain to the platform level. To solve, you need to integrate the weight of each infinitesimal section of the chain over the distance it needs to be raised. Because the chain is uniform, the solution involves setting up and solving an appropriate integral. The work done lifting each portion of the chain will vary based on its starting height off the ground.
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