(Solution) - Three steel cables jointly support a load of 12 k -(2025 Original AI-Free Solution)

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Three steel cables jointly support a load of 12 k (see figure). The diameter of the middle cable is ¾ in. and the diameter of each outer cable is ½ in. The tensions in the cables are adjusted so that each cable carries one-third of the load (i.e., 4 k). Later, the load is increased by 9 k to a total load of 21 k.
(a) What percent of the total load is now carried by the middle cable?
(b) What are the stresses M and O in the middle and outer cables, respectively?