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

We can analyze the forces acting on the beam using the principle of equilibrium, which states that the sum of all forces in any direction and the sum of all torques about any point must be zero for the object to be in static equilibrium (i.e. not moving).

In this case, since the beam is horizontal, we can analyze the forces in the vertical direction. The weight of the beam (120 lb) acts downward, and the force by the cable acts upward. Therefore, the force by the pin on the beam must also act upward and have a magnitude equal to the weight of the beam plus the tension in the cable.

To find the tension in the cable, we can analyze the forces in the horizontal direction. The force by the pin on the beam and the tension in the cable are the only horizontal forces, so they must be equal and opposite by Newton's third law. Therefore, the tension in the cable has a magnitude equal to the force by the pin on the beam.

Using these principles, we can set up the following equations:

ΣF_y = 0: T - 120 lb = 0 (where T is the tension in the cable)
ΣF_x = 0: F_pin - T = 0

Solving these equations for F_pin, we get:

F_pin = T = 120 lb

Therefore, the magnitude of the force by the pin on the beam is 120 lb, which is closest to D) 75 lb.

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