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.

Question

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 1

Consider the cable to be made of four strands of each of three types of wire. Let be the estimated strengths of the wires of the first type, so = 6000 and for i = 1,2,3,4. Let be the estimated strengths of the wires of the second type, so = 5700 and = 30 for =1,2,3,4.Let be the estimated strengths of the wires of the third type, so = 6200 and = 40 for i = 1,2,3,4.



(a) Let D denote the strength of the cable estimated by the ductile wire method.

Then . The uncertainty is



The strength of the cable is 71, 600 ± 108 pounds.



(b) The weakest wire has strength = 5700 ± 30 lbs. The strength of the cable estimated by the brittle wire method, is

= 68,400. The uncertainty is = 12(30) = 360. So B = 68,400 ±360 pounds.