Tension T in a parabolic wire at any point

[ElectronicTeaCup]

Homework Statement:

Assuming that w, the load per horizontal foot, it given, calculate the tension T

Relevant Equations:

See (15,16) below

I am unsure how to go about this. I tried following the suggestion blindly and end up with with some cumbersome terms that are not the answer. From what I understand the derivative at each point would equal to T?

Answer:

I just can seem to get to this. I think I'm there but can't get it in this form

 

[haruspex]

Homework Statement:: Assuming that w, the load per horizontal foot, it given, calculate the tension T
Relevant Equations:: See (15,16) below

View attachment 262705

I am unsure how to go about this. I tried following the suggestion blindly and end up with with some cumbersome terms that are not the answer. From what I understand the derivative at each point would equal to T?

Answer: View attachment 262706 I just can seem to get to this. I think I'm there but can't get it in this form

View attachment 262707

Right at the start you have y on the left instead of y². Correct that and you should get the target answer.

 

What's wrong with their suggestion? I assume you got $T^2 = T_0^2 + w^2 x^2$, and along with $y =\frac{w}{2T_0} x^2$. That should be sufficient to find $T$ in terms of $x$, $y$ and $w$.

 

[ElectronicTeaCup]

Right at the start you have y on the left instead of y². Correct that and you should get the target answer.

Yikes! YES, thanks for the catch! I was so frustrated trying to solve this one.