Chapter 11, Problem 11P

A 120 in.-long beam AB is attached to the wall with a pin at point A and to a 66 in.- long cable CD. A load W=200 lb is attached to the beam at point B. The tension in the cable T and the x and y components of the force at A (F_Axand F_Ay) can be calculated from the equations:

$\begin{array}{l}{F}_{Ax}-T\frac{d}{L_c}=0\\ F_{Ay}-T\frac{\sqrt{L_c^2{d}^2}}{L_c}-W=0\\ T\frac{\sqrt{L_c^2{d}^2}}{L_c}d-WL=0\end{array}$

where L and L_care the lengths of the beam and the cable, respectively, and d is the distance from point A to point D where the cable is attached.

(a) Use MATLAB to solve the equations for the forces T, F_Ax, and F_Ay, in terms of d, L, L_c, and W. Determine F_Agiven by $F_A=\sqrt{F_{Ax}^2+F_{Ay}^2}$.

(b) Use the subs command to substitute W = 200 lb, L = 120 in., and

L_c= 66 in. into the expressions derived in part (a). This will give the forces as a function of the distance d.

(c) Use the ezplot command to plot the forces T and F_A(both in the same figure as functions of d, for d starting at 20 and ending at 70 in.

(d) Determine the distance d where the tension in the cable is the smallest. Determine the value of this force.