Force Vectors: Cable tensions with a hanging weight

[alli.b.]

Question:


Hello!
I am just looking for clarity on whether I have answered this question correctly.

I do not feel like the answer I got, by following an example in the lesson for this practice question, is correct. From my understanding, if the weight is pulling downwards, the tension is less than the weight. I googled whether the tension on the wires by a hanging object could be greater, and the answer I got was no.


Excuse the messy writing, I am typing the question after completing it and wasn't too concerned about my hand writing.
The following is the text before step 3)'s work.
"- since the angles and lengths of the wires are the same, they will have the same tensions. Let T = tension.
2) - the resultant force vector is the equilibrate of the 2500 force vector.
- Create a parallelogram and draw in the resultant force vector.
3) Use sine law and solve for the tension."



This is the example question I followed. It does have two different angles. I figured it would be the same process just without having to solve for separate tensions since the tensions in my question should be the same.



I would love some clarity! And if the answer is correct, but something in the question is wrong it would not be the first time!

Thank you so much!

Cheers,
Alli

 

[HallsofIvy]

Yes, since, as you say the lengths and angles of the wires are equal each will have the same tension and will support half the weight. So each will have a vertical component of 2500/2= 1250 N. You can think of this as a right triangle with one angle 10 degrees and "opposite side' of "length" 1250 N. What is the "length" of the hypotenuse?

 

[alli.b.]

@HallsofIvy
So, in this case, the tension in one wire is 7198.46 N? Would this be an "exception" to the whole "tensions should be less than the weight when the object is hanging" thing?
I did write this out, and I did get the same answer, as following:



Thanks!

 

[Deleted member 4993]

@HallsofIvy
So, in this case, the tension in one wire is 7198.46 N? Would this be an "exception" to the whole "tensions should be less than the weight when the object is hanging" thing?
I did write this out, and I did get the same answer, as following:

View attachment 26379

Thanks!

I do NOT know of a rule that states - whole "tensions should be less than the weight when the object is hanging".

That statement (which I claim does not exist) can be modified to say:

The sum of the vertical components of tensions should be equal to the weight when the object is hanging (in static equilibrium).​

 

[alli.b.]

I do NOT know of a rule that states - whole "tensions should be less than the weight when the object is hanging".

That statement (which I claim does not exist) can be modified to say:

The sum of the vertical components of tensions should be equal to the weight when the object is hanging (in static equilibrium).​

Okay, thanks! I was led to believe it was a thing.