Horizontal beam tension problem please help?

Question

The horizontal beam in the figure weighs 150 N, and its center of gravity is at its center.

http://session.masteringphysics.com/problemAsset/1039065/4/YF-11-27.jpg

Find:

1) Find the tension in the cable.

2) Find the horizontal component of the force exerted on the beam at the wall.

3) Find the vertical component of the force exerted on the beam at the wall.

Answer 1

1)take moments about the hinge on the wall:

(2 x 150) + (4 x 300) - (4 x TsinA) = 0      where T=tension, A=angle between beam and cable

from diagram: sinA = 3/5

300 + 1200 - (12/5)T = 0

1500 = (12/5)T

7500 = 12T

T = 625 N

2) The only other horizontal force on the beam is from the cable. In equilibrium, so force at wall = Hor. force in cable.

Hor force = Horizontal component of T = TcosA

From diagram: cosA = 4/5

So: Hor force = 625 x 4/5 = 500 N

3) In equilibrium:

sum of vertical forces = 0

300 + 150 - TsinA - Y = 0        where Y is vert component at wall

450 - (625 x 3/5) - Y = 0

450 - 365 = Y

Y = 75 N