A uniform 120-lb beam is supported in a horizontal position by a pin and cable as shown in the figure. What is the magnitude of the force by the pin on the beam?
A)94 lb
B)88 lb
C)63 lb
D)75 lb
E)150 lb

Question

A uniform 120-lb beam is supported in a horizontal position by a pin and cable as shown in the figure. What is the magnitude of the force by the pin on the beam? 
A)94 lb 
B)88 lb 
C)63 lb 
D)75 lb 
E)150 lb

Quizplus · Accepted Answer

Since the beam is in a horizontal position, the gravitational force is acting in the downward direction at the center of mass, which is located at the midpoint of the beam. Therefore, the upward force by the cable must be equal and opposite to the gravitational force, which is equal to the weight of the beam:

F_pin = 120 lb - F_cable

We know from the geometry of the situation that the tension force (magnitude) of the cable is the same throughout, so we can use the fact that the vertical force components must balance:

F_cable sin 30° = 120 lb

Solving for F_cable, we get

F_cable = 240 lb / sqrt(3)

Therefore,

F_pin = 120 lb - F_cable = 120 lb - 240 lb / sqrt(3) ≈ 75 lb

So the answer is D) 75 lb.

A Uniform 120-Lb Beam Is Supported in a Horizontal Position