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## Homework Statement

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.

## Homework Equations

ƩM

_{O}= 0

ƩF

_{x}=0

ƩF

_{y}=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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