In: Physics
A 28.0 kg beam is attached to a wall with a hinge while its far end is supported by a cable such that the beam is horizontal. If the angle between the beam and the cable is θ = 57.0° what is the vertical component of the force exerted by the hinge on the beam?
There are 3 vertical forces on the beam. The weight of the beam
is the downward force. The vertical components of the tension in
the cable and the force that hinge exerts on the beam are the
upward forces. For the beam to remain horizontal, the sum of the
upward forces must be equal the weight of the beam. I will assume
that between the beam and the cable is 57˚ above horizontal. Let’s
determine the vertical component of tension in the cable.
Vertical = T * sin 57
Let’s determine the weight of the beam. Weight = 28 * 9.8 = 274.4
N
To determine the vertical component of the tension in the cable, we
will do a torque problem. Let the pivot point be at the hinge.
Let’s assume that the length of the beam is L. The vertical
component of the tension in the cable will produce clockwise
torque. The weight of the beam will produce counter clockwise
torque.
Clockwise torque = T * sin 57 * L
Since the center of mass of beam is at the middle of the beam, the
distance from the hinge to the weight of the beam is L/2.
Counter clockwise torque = 274.4 * L/2
T * sin 57 * L = 274.4 * L/2
T * sin 57 = 137.2
Now we can use the following equation to determine the vertical
component of the force that the hinge exerts on the beam.
137.2 + F = 274.4
F = 137.2 N