A weight W is supported by two cables anchored a distance D apart (see Figure P32). The ca...

A weight W is supported by two cables anchored a distance D apart (see Figure P32). The cable length LAB is given, but the length LAC is to be selected. Each cable can support a maximum tension force equal to W. For the weight to remain stationary, the total horizontal force and total vertical force must each be zero. This principle gives the equations

We can solve these equations for the tension forces TAB and TAC if we know the angles θ and Φ. From the law of cosines

Figure P32

From the law of sines

For the given values D = 6 ft, LAB = 3 ft, and W = 2000 lb, use a loop in MATLAB to find LACmin, the shortest length LAC we can use without TAB or TAC exceeding 2000 lb. Note that the largest LAC can be is 6.7 ft (which corresponds to θ = 90°). Plot the tension forces TAB and TAC on the same graph versus LAC for LACmin ≤ LAC ≤ 6.7.