Equilibrium and gravity on a uniform beam

[alexandertg6]

Homework Statement

a uniform beam of length 12.0 m is supported by a horizontal cable and a hinge at angle θ = 70° with the vertical. The tension in the cable is 500 N. Find the gravitational force on the beam in unit vector notation and the force on the beam from the hinge in unit vector notation.

Homework Equations

force from gravity = mg
vertical force on beam from hinge = mg
Horizontal component of gravity = 0
horizontal component of force of hinge on beam = 500N

The Attempt at a Solution

I know that the horizontal force on the beam has to be in equilibrium with the tension of the cable.

T = .5(horizontal distance) ( gravity) (mass)/ vertical distance
500 = (.5(9.8)(12sin70)m)/(12cos70)
m= 37.13
mg = 363 but its wrong =\

 

[tiny-tim]

Welcome to PF!

Hi alexandertg6! Welcome to PF!

a uniform beam of length 12.0 m is supported by a horizontal cable and a hinge at angle θ = 70° with the vertical. The tension in the cable is 500 N. Find the gravitational force on the beam in unit vector notation and the force on the beam from the hinge in unit vector notation.
…
T = .5(horizontal distance) ( gravity) (mass)/ vertical distance
500 = (.5(9.8)(12sin70)m)/(12cos70)

hmm … you've taken moments about the hinge …

but what's 12sin70º ?