Solving Tension of Cable Supporting 56kg Beam - kN

[o0ojeneeo0o]

Homework Statement

Two weights attached to a uniform beam of mass 56 kg are supported in a horizontal position by a pin and cable as shown in the figure.The acceleration of gravity is 9.8 m/s2 .

What is the tension in the cable which supports the beam? Answer in units of kN.

Homework Equations

The Attempt at a Solution

here's what I have thus far... I'm sorry, I know it's not much!

Known:
Mbeam= 56k
Mass 1 = M1 = 22kg
Mass 2 = M2 = 59kg
Force of M1 = F1 = M1g = 215.6N
Force of M2= F2 = M2g = 578.2N
ΣFy = 0
ΣFx = 0
ΣFτ = 0
If ΣFy = 0, then:
0 = Fcy – mg – F1 – F2
If ΣFτ = 0, then:
0 = -mg(4.2m) – F1g(2.6m)

I'd really love it if someone could solve this for me, but it would be even better if someone could walk me through how to get the answer because I honestly have no clue!

Thank you in advance!

 

[Delphi51]

It is a mistake to use ΣFy = 0 because you don't know what force acts at the pivot point on the wall. Instead, use the sum of the torques = 0. Take the torques about that pivot point marked with a big black dot.

 

[nlightner]

Hello,

To solve this problem, we can use the principles of static equilibrium. This means that the beam and weights are not moving, so the sum of all forces and torques acting on them must be equal to zero.

First, we need to draw a free body diagram of the beam and weights. We can label the tension in the cable as T, and the distance between the pin and the center of mass of the beam as d.

Now, we can write out the equations of static equilibrium:

ΣFy = 0 : This means that the sum of all forces in the y-direction must be equal to zero.

T - Mbeam*g - M1*g - M2*g = 0

ΣFτ = 0 : This means that the sum of all torques must be equal to zero.

-T*d + Mbeam*g*d + M1*g*(d/2) + M2*g*(d/2) = 0

We can solve these equations simultaneously to find the tension in the cable, T.

T = (Mbeam*g + M1*g + M2*g) / (1 + d/d + d/2 + d/2)

T = (56*9.8 + 22*9.8 + 59*9.8) / (1 + 4.2 + 2.6 + 2.6) = 1474.8 N

To convert this to kN, we can divide by 1000.

T = 1474.8 / 1000 = 1.47 kN

Therefore, the tension in the cable supporting the beam is 1.47 kN. I hope this helps!