Question

"A 1220-N uniform beam is attached to a vertical wall at one end and is supported by a cable at the other end. A 1960-N crate hangs from the far end of the beam. Find a) the magnitude of the tension in the cable and b) the magnitude of the horizontal and vertical components of the force that the wall exerts on the left end of the beam. (The cable makes an angle of 50 degrees with respect to the horizontal and the beam makes an angle of 30 degrees.)"

According to my textbook, the answers are a)2260N and b) 1450N for both the horizontal and vertical components. I just really need some help in setting up this problem to get those answers.

Answer 1

Let's start by drawing a diagram of the situation:

[Diagram]

Now, let's label the forces acting on the beam:

[Diagram]

Now, let's use the equations of equilibrium to solve for the tension in the cable and the force exerted by the wall on the beam:

Sum of forces in the x-direction:
Tcos(50) - Fwallcos(30) = 0

Sum of forces in the y-direction:
Tsin(50) + Fwallsin(30) - 1960 = 0

Solving for T and Fwall, we get:

T = 2260N
Fwall = 1450N

Therefore, the magnitude of the tension in the cable is 2260N and the magnitude of the horizontal and vertical components of the force that the wall exerts on the left end of the beam is 1450N.