(Solved): A \( 1,000 \mathrm{~N} \) dowel is held in place by a light cable at an angle \( \theta=25.5^{\cir ...

A \( 1,000 \mathrm{~N} \) dowel is held in place by a light cable at an angle \( \theta=25.5^{\circ} \) to the horizontal as shown in the figure. The dowel is attached to a pivot at the bottom, and a mass of weight \( w=2,250 \mathrm{~N} \) hangs from its top. The dowel makes an angle of \( \varphi=64.5^{\circ} \) with the horizontal. Assume dowel is uniform. (a) Find the tension in the supporting cable (in kN). \[ \mathrm{kN} \] (b) Find the components of the reaction force (in kN) exerted by the floor on the dowel. horizontal component: magnitude \( \mathrm{kN} \) direction vertical component: magnitude \( \mathrm{kN} \) direction