A 1390-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. Using the data shown in the figure, find (a) the magnitude of the tension in the wire and the magnitudes of the (b) horizontal and (c) vertical components of the force that the wall exerts on the left end of the beam.

Have to know cable angle from vertical

1250

To solve this problem, we can use the principles of equilibrium to find the required values.

First, let's consider the forces acting on the beam. There are three forces to consider: the weight of the beam itself, the tension in the wire, and the weight of the crate hanging from the beam.

(a) To find the magnitude of the tension in the wire:

Since the beam is in equilibrium, the sum of the forces in the vertical direction must be zero. The only vertical force acting on the beam is the tension in the wire. The weight of the beam and the crate cancel each other out because they both act vertically in opposite directions.

So, we have:

Tension in wire – Weight of beam – Weight of crate = 0

Tension in wire = Weight of beam + Weight of crate
Tension in wire = 1390 N + 1960 N
Tension in wire = 3350 N

Therefore, the magnitude of the tension in the wire is 3350 N.

(b) To find the horizontal component of the force that the wall exerts on the left end of the beam:

Since the beam is in equilibrium, the sum of the forces in the horizontal direction must be zero. The only horizontal force acting on the beam is the horizontal component of the force exerted by the wall.

So, we have:

Horizontal component of force by wall – 0 = 0

Therefore, the horizontal component of the force that the wall exerts on the left end of the beam is 0 N.

(c) To find the vertical component of the force that the wall exerts on the left end of the beam:

Since the beam is in equilibrium, the sum of the forces in the vertical direction must be zero. The only vertical force acting on the beam is the vertical component of the force exerted by the wall, which counteracts the weight of the beam and the crate.

So, we have:

Vertical component of force by wall – Weight of beam – Weight of crate = 0

Vertical component of force by wall = Weight of beam + Weight of crate
Vertical component of force by wall = 1390 N + 1960 N
Vertical component of force by wall = 3350 N

Therefore, the magnitude of the vertical component of the force that the wall exerts on the left end of the beam is 3350 N.