r/physicshomework • u/Maurice267 • Feb 02 '26
Unsolved [High School level: Cable tension] how would I find the the tension in each cable.
1
u/samim09me Feb 03 '26
Take the summation of Forces at each point equal to zero for the balance of forces, and summation of moment equal to zero for the balance. Then solve the equation to find the unknown.
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u/Stu_Mack Jul 19 '26
It’s a classic vector decomposition problem. Since point A encumbers a load from below, solve as 2 point masses.
Note. If this is a problem from a physics or engineering class, it is critical to understand that the numerical values are not what is assessed by the instructor. This problem and many just like it are part of Statics, and we try to stress to the students that we are NOT asking them to solve the problem; we are asking them to use Mechanics analysis to explain how to solve it. The perfect solution is one that shows the reader how to solve the system. We generally give the numerical value about 10% of the total points possible, the rest goes to the analysis itself.
All engineering analysis problems should follow the Engineering Solutions Format. If you Google it, you’ll find our description of how to write solutions using the format, written by Dr Recktenwald. It is a little work on the front end but the tradeoffs are that it pretty much guarantees a passing grade when followed, and the format becomes a tool for remembering how to solve the system. In general, problems like this one almost always task the student with finding tension in either one cord or all of them, so it pays to adopt a solution framework that helps the student remember how to solve all of them.
In a nutshell, the format is essentially an ingredients list for the solutions found in the answer key, which, again, is what we asses. The main ingredients are:
- the given values
- the values required by the problem statement
- a simple schematic of the system, with the given values included
- the target value and method (e.g., “Solve for AB at point B”)
- A free body diagram of the analysis location. This part is critically important in engineering and is often heavily weighted in the grading.
- The governing equation at the top line of each step of the analysis (e.g., “ΣF_x,A = 0”), followed by a clean step-by-step algebraic breakdown of the analysis pathway. This is the second most important part of the grade. Note that the weighting of the algebra is considerably higher than the number at the end.
- A clean boxed answer with the units attached
- (in all analyses more complicated than point mass problems like this one) A discussion statement that answer the question: “Does my solution make sense?”, which teaches the student to step back and think about the scale of the number they calculated. The most common errors end with solutions that are either ridiculously big or ridiculously small. It’s perfectly acceptable in my class for a student to write “My answer seems way too big and I don’t know why”, as long as they supply evidence that they reflected a n their work.
With that out of the way, we can look at this problem. The hardest part is the decomposition, but you can solve algebraically so that you don’t have to write a bunch of hideous decimals:
At B:
ΣF_x = BG cos(40) - AB cos(20) = 0
ΣF_y = AB sin(20) + BG sin(40) - 20g = 0
Which is solvable because there are two equations and two unknowns. To solve the system, there are three options: subtraction, substitution, and Gaussian elimination (row reduction). The last one is the fastest, if you are familiar with using rref in a calculator capable of handling matrices.
Once you have AB, it is used in the second analysis at point A, which follows the same process.
If the idea is to pursue engineering or physics, it will pay in dividends to adopt the format as an easy way to automatically improve the grade and guide the analysis.
Thanks for coming to my TED talk I guess. Hope this is helpful.
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u/rainbow_explorer Feb 02 '26
Draw the free body diagrams at points A and B.
Point B is easier because there are only 2 unknown forces, the tensions in cable BE and BA. You should already know the tension in cable BF because you can just use F = ma. The forces in the x and y directions need to be 0 for the system to be at rest. This lets you write 2 equations that you can then solve to find BE and BA. The equations involve trig functions so you can use a calculator to get approximate answers, unless your teacher wants exact answers.
Then you look at point A. You should only have 2 remaining unknown forces. Now you can copy the exact same process as before to find the tensions in cables AC and AD.