Find the tension \(T\) in each cable and the magnitude and direction of the force exerted on the strut by the pivot in each of the arrangements in Fig. E11.13. In each case let \(w\) be the weight of the suspended crate full of priceless art objects. The strut is uniform and also has weight \(w\). Start each case with a free-body diagram of the strut.

Step 1 of 5

(a)

The free-body diagram is as follows:

The net torque at the pivot is given by:

\(\sum \tau=T L \sin 30^{\circ}-w L / 2 \cos 30^{\circ}-w L \cos 30^{\circ}=0\)

\(T \sin 30^{\circ}-\frac{3}{2} w \cos 30^{\circ}=0\)

\(T \sin 30^{\circ}=\frac{3}{2} \cos 30^{\circ}\)

\(T=\frac{3}{2} w \cot 30^{\circ}\)

\(T=2.6 w\)