Hinges Cable
Hinges Cable
A 27.8 kg beam is attached to a wall with a hinge and its far end is supported by a cable such?
A 27.8 kg beam is attached to a wall with a hinge and its far end is supported by a cable such that the angle between the beam and the cable is 90o. If the beam is inclined at an angle of theta = 23.7o with respect to horizontal, what is the magnitude of the horizontal component of the force exerted by the hinge on the beam?
Let L = length of the beam
T = tension in the cable
Fh = horizontal component of force by the hinge
Fv = vertical component of force by the hinge
Take counterclockwise torque as positive. Let us find torques around the hinge.
Torque by T = T L
Torque by the force of gravity = -m g L/2 * cos(theta)
Torque by Fh = 0
Torque by Fv = 0
Net torque = 0
Therefore, T L - m g L/2 * cos(theta) = 0
Dividing both sides by L,
T - m g/2 * cos(theta) = 0
T = mg/2 * cos(theta) --------------------(1)
The cable makes 90 deg - theta with the horizontal.
Net horizontal force = 0
Therefore Fh - T cos(90 deg - theta) = 0
Fh - T sin(theta) = 0
Fh = T sin(theta) --------------------------(2)
Substituting the value of T from equation (1) into equation (2):
Fh = mg/2 * cos(theta) * sin(theta)
Fh = 27.8 * 9.8/2 * cos(23.7 deg) * sin(23.7 deg)
Fh = 50.1 N
Ans: 50.1 N
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