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Horizontal beam supported by a hinge and a string: static equilibrium beam and cable problem.
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In this classic hinged beam and cable problem, we are given a horizontal beam supported by a hinge and a string. The goal is to find the tension in the string and the magnitude of the hinge force.
We begin by using the hinge as the rotation axis for the torque analysis. We have two clockwise torques: the torque exerted by the force of gravity pulling down on the suspended mass of 5kg and the torque due to gravity acting on the center of mass of the beam itself. In the counterclockwise direction, we have the torque exerted by the vertical string. We set the clockwise torques equal to the counterclockwise torques and quickly solve for the tension in the vertical cable.
The natural next question in a static equilibrium beam and cable problem is to find the force exerted by the hinge. We show qualitatively that the hinge force must point downward by choosing a new rotation axis for the analysis of torque on the beam. Finally, we analyze forces in the y direction to find the magnitude of the force exerted by the hinge.
We begin by using the hinge as the rotation axis for the torque analysis. We have two clockwise torques: the torque exerted by the force of gravity pulling down on the suspended mass of 5kg and the torque due to gravity acting on the center of mass of the beam itself. In the counterclockwise direction, we have the torque exerted by the vertical string. We set the clockwise torques equal to the counterclockwise torques and quickly solve for the tension in the vertical cable.
The natural next question in a static equilibrium beam and cable problem is to find the force exerted by the hinge. We show qualitatively that the hinge force must point downward by choosing a new rotation axis for the analysis of torque on the beam. Finally, we analyze forces in the y direction to find the magnitude of the force exerted by the hinge.
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