The horizontal beam in the figure weighs 150 N, and its center of gravity is at its center
The horizontal beam depicted in the figure weighs 150 N, and its center of gravity is located at its midpoint. Please solve the following problems:
1) Determine the tension in the cable.
2) Calculate 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.
1 Answers
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
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