Beam hinged to wall with a cable (torque, etc)

[lizzyb]

Hi. I've tried to answer this questions four times and so far none of my answers have been correct. Any help is greatly appreciated!

A uniform 48 kg (m) beam at an angle of 24 degrees (theta) with respect to the horizontal has length of 38 m (L). It is supported by a pin and horizontal cable. The acceleration of gravity is 9.8 m/s^2 (g). What is the magnitude of the total force exerted by the pin on the beam?

So far:

$$\sum F_x = F_h - T = 0$$ horizontal component of pin - tension of cable
$$\sum F_y = F_v - mg = 0$$ vertical component of pin - mass of beam * gravity
$$\sum \tau = \sin \theta L T - \cos \theta L m g = 0$$

Does this look ok to you? For the torque, I'm trying to use the moment arm times the magnitude of the force.

Thank you.

 

[lizzyb]

The last equation should have been:
$$\sum \tau = \sin \theta L T - \cos \theta \frac{L}{2} m g = 0$$
and that took care of it.