A 226kg uniform beam is hinged at one end and the other is supported at a cable

Question

A 226kg uniform beam is hinged at one end and the other is supported at a cable that is 30 degrees to the vertical. The beam is 2m long and is at 8 degrees above horizontal. Calculate the direction of the force measured with respect to the horizontal at the hinge. A 226kg uniform beam is hinged at one end and the other is supported at a cable that is 30 degrees to the vertical. The beam is 2m long and is at 8 degrees above horizontal. Calculate the direction of the force measured with respect to the horizontal at the hinge.

Explanation / Answer

Let tension in cable be T. writing torque equation about hinge,

T sin (90 - 30 + 8) degree * L = mg L/2 cos 8 degree

T = 226*9.8/2 * cos 8 degree / sin 68 degree = 1183 N

Fx = T sin 30 degree = 591.5 N

Fy = mg - T cos 30 degree = 1183 - 1024.5 = 158.5 N

angle = arctan(158.5/591.5) = 15 degree answer

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