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A Beam on Wall

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A 30.8 kg beam is attached to a wall with a hinge and its far end is supported by a cable. The angle between the beam and the cable is 90o. If the beam is inclined at an angle of q = 24.5o with respect to horizontal, what is the horizontal component of the force exerted by the hinge on the beam? (Use the `to the right' as + for the horizontal direction.)

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The physics of this problem is that the beam is in equilibrium, so both net force equals 0 and also net torque equals zero about any axis. The angle in your posting is given as q= 24.5 degrees.
On your diagram, choose an axis at the hinge. For this ...

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