Equilibrium. How to solve for four variables?

[moose726]

Homework Statement

One end of a uniform beam weighing 288 N and 3.12 feet long is attached to a wall with a hinge. The other end is supported by a wire making equal angles of 30° with the beam and wall.

(a) Find the tension in the wire.

(b) What is the horizontal component of the force of the hinge on the beam?

(c)What is the vertical component of the force of the hinge on the beam?

Homework Equations

$$\Sigma$$F=0
$$\Sigma$$$$Torque$$=0

The Attempt at a Solution

I drew a free body diagram of the beam and the components of the forces from tension and the hinge. From this I got four equations:
$$\Sigma$$F_x = F_x-T_x = 0
$$\Sigma$$F_y = F_y+T_y-mg = 0
$$\Sigma$$ Torque = 118.5+.4754T_x-.823T_y=0 (T is tension, this torque is with the hinge as the origin.)
F_y=F_xtan(30)
I'm not sure how to solve for each variable with these equations.

 

[Bacat]

The easiest way to think about this is to break it into parts. Instead of solving for multiple unknowns just solve for part a.

The vertical component of tension must be perfectly balanced by the vertical component of the torque of the beam. Same goes for the horizontal tension.

You can calculate the torque in the x and y directions and then you have two equations with two unknowns.

 

[rl.bhat]

Take the components of tension T along and perpendicular to the beam. Similarly take the components of the weight of the beam, which acts at the center of the beam.
The perpendicular components contribute to the torque, while components along the beam does not contribute to the torque.
Apply the condition for equilibrium and solve for T.
Convert the unit of length from ft to m.