A cable of length Lc supports a beam of length Lb, so that it is horizontal when the weigh...

A cable of length Lc supports a beam of length Lb, so that it is horizontal when the weight W is attached at the beam end. The principles of statics can be used to show that the tension force T in the cable is given by

where D is the distance of the cable attachment point to the beam pivot. See Figure P24.

Figure P24

a. For the case where W = 400 N, Lb = 3 m, and Lc = 5 m, use element-by-element operations and the min function to compute the value of D that minimizes the tension T. Compute the minimum tension value.

b. Check the sensitivity of the solution by plotting T versus D. How much can D vary from its optimal value before the tension T increases 10 percent above its minimum value?