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 state of equilibrium, the sum of the forces acting on it must be zero. The weight of the beam, acting downwards at its center of gravity, has a magnitude of 120 lb. The tension force in the cable, acting upwards at an angle of 30 degrees, can be resolved into horizontal and vertical components using trigonometry:

Tcos(30) = F_horizontal
Tsin(30) = F_vertical

Since the beam is not accelerating horizontally, F_horizontal = 0. Therefore, Tcos(30) = 0, which means T = 0 or cos(30) = 0.5.

Since the beam is in a state of equilibrium, the sum of the forces acting on it must be zero. Therefore, the magnitude of the force by the pin on the beam is equal in magnitude and opposite in direction to the vertical component of the tension force:

F_pin = -F_vertical = -Tsin(30) = -(120 lb)(0.5) = -60 lb

However, we are asked to find the magnitude of the force, not its direction, so we take the absolute value:

|F_pin| = 60 lb

Since the force by the pin on the beam is downwards, the correct answer is:

Answer: D) 75 lb

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