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A cable is made up of several parallel strands of wire.

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 14SE Chapter 3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 14SE

A cable is made up of several parallel strands of wire. The strength of the cable can be estimated from the strengths of the individual wires by either of two methods. In the ductile wire method, the strength of the cable is estimated to be the sum of the strengths of the wires. In the brittle wire method, the strength of the cable is estimated to be the strength of the weakest wire multiplied by the number of wires. A particular cable is composed of 12 wires. Four of them have strength 6000 ± 20 lb, four have strength 5700 ± 30 lb, and four have strength 6200 ± 40 lb.

a. Estimate the strength of the cable, and find the uncertainty in the estimate, using the ductile wire method.

b. Estimate the strength of the cable, and find the uncertainty in the estimate, using the brittle wire method.

Step-by-Step Solution:

Answer :

Step 1 of 3 :

Given,

The cable is made up of several parallel strands of wir. The particular cable is composed of 12 wires. Four of them have 6000 20lb. Four have strength 570030 lb, and another four have strength 620040 lb.

The goal of the problem is

Find the strength of the cable, and uncertainty in the estimate, using the ductile wire method.Find the strength of the cable, and uncertainty in the estimate, using the brittle wire method

Step 2 of 3 :

The claim is to find the strength of the cable, and uncertainty in the estimate, using the ductile wire method.

We can find the strength of the cable using ductile wire method.

The strength of the cable is estimated to be sum of the strength of the wires.

That is,   L = 4X + 4Y + 4Z

Where, X = 6,000  Y = 5,700  and  Z = 6,200

Let, L = 4(6000) + 4(5700) + 4(6200)

           = 71,600

Therefore, the strength of the cable is 71,600

For uncertainty

 =

Where,  = (20 ,   = (30 and    = (40

Therefore,  =

                        =

                       = 107.70  108.

Hence, the strength of the cable is 71,600 lb and the uncertainty of the estimate is 108.

Step 3 of 3

Chapter 3, Problem 14SE is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: Strength, cable, Wire, method, estimate. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The answer to “A cable is made up of several parallel strands of wire. The strength of the cable can be estimated from the strengths of the individual wires by either of two methods. In the ductile wire method, the strength of the cable is estimated to be the sum of the strengths of the wires. In the brittle wire method, the strength of the cable is estimated to be the strength of the weakest wire multiplied by the number of wires. A particular cable is composed of 12 wires. Four of them have strength 6000 ± 20 lb, four have strength 5700 ± 30 lb, and four have strength 6200 ± 40 lb.a. Estimate the strength of the cable, and find the uncertainty in the estimate, using the ductile wire method.________________b. Estimate the strength of the cable, and find the uncertainty in the estimate, using the brittle wire method.” is broken down into a number of easy to follow steps, and 147 words. The full step-by-step solution to problem: 14SE from chapter: 3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 14SE from 3 chapter was answered, more than 300 students have viewed the full step-by-step answer.

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