Component Wall A uniform beam of weight 196N and of length 1.00m is attached to a hinge on the outside wall of the restaurant?
A cord is attached at the center of the beam and is attached to the wall, making an angle of 30.0degrees with the beam. The cord keeps the beam perpendicular to the wall. If the breaking tension of the cord is 620N, how large can the mass of the sign be without breaking the cord? Find the vertical component of the force exerted by the hinge in two different ways: a) setting the net force equal to zero and b) using a torque equation about a different axis.
Draw the Free Body Diagram and put a roller on the hinge with a force pushing UP. That is the vertical reaction of the wall on the hinge
Our first problem is find that vertical reaction.
Assume since the beam is uniform that its CG is at 0.5 m. Add a vector down at the CG = 196 N
Draw a vector (the cord) at 30 degrees from the CG back to the wall label it 640 N.
Now do the trig and resolve the horizontal (Which we don't need for your problem, but we will come back to it) and vertical components of that 620N tension in the cord:
sin 30 = Fx/620
Fx = 0.5 * 620 = 310 N
Assume the sign is symetric around the CG of the beam. ===> its CG is also at 0.5 m (You did NOT say otherwise, so I can put it anywhere I want.)
Sum Fx = Wsign + Wbeam - Fx - Fxwr (wall reaction x)
Sum Fx = Ws + 196 - 310 N - Fxwr
But Fxwr must be zero since Ws + Wb = maximum x component in cord ===> Ws = 114 N The hinge vertical force = 0 (If the cord were vertical the beam would balance with both ends free (We'll come back to this.) All the x forces occur at the CG of the sign and beam.
Sum Me (Sum Moments about free end)
Me = .05 *(196 + 114) [CW] - 0.5 * Fx [CCW]
Me = .05 * 310 - .05*310 = 0
So what is going on at the hinge? There was a horizontal force component from the cord. But, nobody asked about that. The wall is pushing out against the beam with
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