A beam and cable support a crate weighing $\backslash ($ W$=1000\backslash$mathrm$\{$lb$\}\backslash )$ hanging at the position shown. A moment $\backslash ($ M$=500\backslash$mathrm$\{$ft$\}-\backslash$mathrm$\{$lb$\}\backslash )$ is applied at the mid$-$span of the beam. The weight of the beam and cable are negligible.

a$)$ Draw the free$-$body diagram of the system. Define your coordinate system. $($Draw a separate sketch, not on the drawing provided$).$

b$)$ Determine the tension in the cable and the reactions at $\backslash ($ A $\backslash ).$