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.

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 methodStep 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.