Solve for Tension in 3-Cable System on 120 ft Tower Using Trigonometry

[r34racer01]

1. A 120 ft tower is being held by three cables in tension. Cable AO is in 1000
lb of tension. Find the tension in the other cables and the vertical force from
the tower if the whole system is at rest.

3. So using lots and lots of trig I was able to find most of the magnitudes, thetas, and phi's as you can see from the last 2 images. But now I'm lost from there. During office hrs. my prof. mentioned something about using unit vectors and then labeling the pts. A, B & C as coordinates A(-30,0,-20), b(-20,0,20), & c(40,0,10), but I don't see how those can help me. Any suggestions?

 

[nvn]

Hi, r34racer01. The PF rules state we are not allowed to tell you how to approach or solve your homework problem. You must list relevant equations yourself, and show your calculations to determine the forces; and then someone might check your math.

 

[Mene]

I would suggest approaching this problem by breaking down the forces acting on the tower and cables into their components. This will help simplify the problem and make it easier to apply trigonometric principles.

First, let's label the points A, B, and C as mentioned in the problem. We can also label the angle between cables AB and AC as theta, and the angle between cable AB and the horizontal as phi.

Next, we can draw a free body diagram of the tower and cables, showing all the forces acting on the system. This will include the tension in cable AO (1000 lb), the tension in cable AB (unknown), the tension in cable AC (unknown), and the vertical force from the tower (unknown).

Using trigonometric principles, we can then write equations for the forces in the x and y directions. For example, in the x direction, we can write:

Tension in cable AB * cos(theta) + Tension in cable AC * cos(phi) = 0

Similarly, in the y direction, we can write:

Tension in cable AB * sin(theta) + Tension in cable AC * sin(phi) + Vertical force from tower = 0

We now have two equations and three unknowns (tension in cable AB, tension in cable AC, and vertical force from tower). We can solve for these unknowns by using the third equation given in the problem, which states that the system is at rest. This means that the sum of all forces in both the x and y directions must equal 0.

Solving these equations simultaneously will give us the tension in cable AB, tension in cable AC, and the vertical force from the tower. We can then use these values to find the remaining angles and magnitudes using trigonometric principles.

In summary, the key to solving this problem is to break it down into smaller components and use trigonometry to find the unknowns. By carefully labeling the points and angles and drawing a free body diagram, we can simplify the problem and find the desired values.