The cable ABCD of length L = 18.6m supports two street lights of weight W = 1kN each. Given L1 = L2 = 6m, L3 = 4m, d = 1m we need to find the tensions in the three cable segments and the sags y1, y2. Neglect the weight of the cable.
http://i43.tinypic.com/315bbrp.png
http://i43.tinypic.com/315bbrp.png
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Break the problem into two diagrams.
The first includes Cables T1 and T2 and the second includes T2 an T3.
For the cables T1(AB) and T2(BC) find the SumFx and SumFy forces and solve for T1(AB) and (BC). You will need to solve two equations for 2 unknowns. Note that Fy must include the weights of the lights.
Then do the same for the cables T2(BC) and T3(CD) by finding the SumFx and SumFy forces, but you already know what T2(BC) is from the previous solution for T1 and T2.
The first includes Cables T1 and T2 and the second includes T2 an T3.
For the cables T1(AB) and T2(BC) find the SumFx and SumFy forces and solve for T1(AB) and (BC). You will need to solve two equations for 2 unknowns. Note that Fy must include the weights of the lights.
Then do the same for the cables T2(BC) and T3(CD) by finding the SumFx and SumFy forces, but you already know what T2(BC) is from the previous solution for T1 and T2.