How to Find the Cable Tension Forces - Static Equilibrium - Equilibrium Problem 3

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In this video, we find the tension in the cables shown due to the applied force on the system. This problem is solved using static equilibrium and the property that all forces, internal and external, must cancel and counteract each other so all forces sum to be zero.
Problem statement:
Two cables are tied together at C and loaded as shown. Determine the tension in AC and BC.
Problem walkthrough steps:
Draw a free body diagram
Look at each force separately, known and unknown
Find or determine the x and y directional forces for each of the known and unknown forces in variable form
Sum all the x directional forces together. Then sum all the y directional forces together
Solve for the unknown forces. Can use multiple processes to solve for 2 equations 2 unknowns (if this happens)
Check answers
Topics of this problem include:
Free Body Diagram (FBD)
Solve a statics equilibrium problem with multiple unknowns
Determining equilibrium
2 unknown forces
2 unknown vectors
X and Y Components
Summation of forces in the x and y directions
Vector Addition
Force combination
Vector combination
Vector Mechanics
Forces in right triangles
Orthogonal vectors
Determining tension forces
Summing forces to be zero
Beer Johnston problem 2.33
Engineering statics
2D equilibrium problem 3
College level
Professor Engineer
Professor_Engineer

[@Professor_Engineer]

Thanks for watching! Don't forget to like this video, subscribe to the channel, and leave a positive comment below! Also, if this video was helpful, please use the link to view the next problem in this Static Equilibrium Series:
ruclips.net/video/U41vsiX2do8/видео.html

[@stoffeundeis5208]

THATS AMAZIG. Please keep going. The german engeneer static videos are very dry and dont use numbers. That's why I am looking for english videos, and yours is just perfect. Thank you!

[@Professor_Engineer]

Awesome! Glad I could help!

[@HarryKaufman-go2nx]

Glad I found this channel. So helpful👍

[@mayghazi8210]

Thank youuuu!!

[@alitr-tf1dc]

thanks a lot 💙

[@sirig03]

Thank you so much

[@Professor_Engineer]

No problem!

[@Marv_33]

thanks for the great explanation I will use this channel and shared with some of my current classmates.

[@Professor_Engineer]

Great, hope my channel helps everyone!

[@sandrashappell6754]

Why didn't you include the gravitational force on 300? Is it just a choice? Does including it just change the unit such as newtons?

[@Professor_Engineer]

Since this problem is in US Customary Units, we do not include the acceleration of gravity on weights in units of force such as pounds (lbs), kips (k) or tons. In the SI system, we need to include/multiply by the acceleration of gravity on masses such as kilograms (kg) to convert these masses into forces, which would be Newtons. In US Customary Units, if we were given a mass, which would be in units of slugs, then we would have to multiply by the acceleration of gravity. So, in short, when in force units do not multiply by the acceleration of gravity. I hope this helps.

[@scisev]

aren’t the angles wrong? shouldn’t it be 90-20 and 90-40

[@Professor_Engineer]

The angles shown are correct. And hopefully this explanation helps, think of the cable as a transversal line going through the solid black horizontal line at point A where the 40 degrees is measured and going through the x-axis at point C where I drew the free body diagram. Because that solid horizontal line and the x-axis on the FBD are parallel to each other, any line crossing both of these parallel lines will be transversal. Thus, the angle between the parallel line and the transversal line (on the interior side of the crossing) will be equal at each end. Basically, if the line of the cable is 40 degrees of the horizontal at one location, it will be that same 40 degrees off the horizontal at another location. If you need a better explanation, let me know. Hopefully this helped.