uniform 155-kg beam is freely hinged about its upper end A and is initially at r

Question

uniform 155-kg beam is freely hinged about its upper end A and is initially at rest in the vertical position with ? = 0. Determine the initial angular acceleration ? (positive if counterclockwise, negative if clockwise) of the beam and the magnitude FA of the force supported by the pin at A due to the application of a force P = 253 N on the attached cable.

The uniform 155-kg beam is freely hinged about its upper end A and is initially at rest in the vertical position with theta = 0. Determine the initial angular acceleration a (positive if counterclockwise, negative if clockwise) of the beam and the magnitude FA of the force supported by the pin at A due to the application of a force P = 253 N on the attached cable.

Explanation / Answer

Torque at theta = 0 is

Pcos45*5 = I*alpha = (ML^2/3)*alpha = (155*6.7^2/3)*alpha

P = 656*alpha

alpha = 253/656 = 0.385rad/s^2

Force at A = mg - Psin45 = 155*9.8 - 253*(1/sqrt2) = 1340.1N

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