Torque problem

PhysicsinCalifornia

A 20.0 kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole. A cable at an angle of 30.0[tex]\circ[/tex] with the beam helps to support the light. Find (a) the tension in the cable and (b) the horizontal and vertical forces exerted on the beam by the pole.

This is what I got so far:
[tex]\sum F_y = T\sin30.0\circ - W = 0[/tex]
[tex]\sum F_y = T(\frac{1}{2}) = 196 N[/tex]
[tex]T = 392 N[/tex]

I'm having trouble with part (b). I know I'm supposed to use [tex]\sum\tau = 0[/tex] but I'm getting stuck because I don't know what to use for the moment arm(if I'm supposed to)

Anything would help, thanks in advance

Pyrrhus

Are you sure part A is correct? you seem to have ignored the articulation support reaction (at the hinge). Remember the vector representation of the reaction has two components.

Now about the torque, you haven't provided any distances, but if you do, i would take moment about the hinge, so i can find teh Tension, then i would use sum of forces to find both reactions at the hinge, obviously the component parallel to the x axis will be equal to the component parallel to the axis of the Tension force.

andrevdh

I agree with your answer to (a). For part (b): You can solve it by using components only. There are 2 unknowns, the magnitude of the reaction force on the beam at the hinge and the angle that the force makes with the beam. Therefore you should be able to solve the problem with two equations (the force components must be zero in order for the beam to be in equilibrium).