To test the deflection of the uniform 270-lb beam the 120-lb boy exerts a pull of 35 lb on the rope rigged as shown. Compute the force supported by the pin at the hinge O.
I have attached an image of the question.
ƩMO = 0
The Attempt at a Solution
My first thought is to find the moment about point O, for which I could then solve for the force at point A.
0 = -A(1.9') + (270lb)(5.45') + T(8.5') + (120lb)(7.0')
A = 1373.157 lb
However I'm not sure whether I have the right center of gravity of the beam, because I'm unsure whether the ball at point A (or whatever that is) alters it. So would the center of gravity of the beam be at 5.45' or at 4.5'?
Also, am I correct in assuming that the 35lb force that the boy applies to the rope is transferred completely to the rope that is 8.5' away from O?
Assuming that I am correct, I did the following then found the force in the y direction at the point O, Fo
0 = Foy +Ay -270lb -120lb -35lb
Foy = -Ay + 270 + 120 + 35
F0y = -948.157895
I tried entering 948.15 as I had thought that perhaps it wanted the magnitude of the force but it didn't accept this.
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