# Tension T in a parabolic wire at any point

• ElectronicTeaCup
In summary, the conversation discusses a problem with finding the tension T in terms of x, y, and w, and suggests using equations (15,16) to solve it. However, there is an error in the given suggestion regarding the use of y instead of y2. The conversation ends with the suggestion to correct the error in order to obtain the target answer.
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?

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

ElectronicTeaCup said:
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.

ElectronicTeaCup
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##.

Last edited by a moderator:
ElectronicTeaCup and Delta2
haruspex said:
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.

## 1. What is a parabolic wire?

A parabolic wire is a type of wire that has a parabolic shape, meaning it curves in a symmetrical arc. It is commonly used in engineering and construction for its strength and stability.

## 2. How is tension T calculated in a parabolic wire?

Tension T in a parabolic wire is calculated using the equation T = mg + (mL^2/8h), where m is the mass of the wire, g is the acceleration due to gravity, L is the length of the wire, and h is the height of the wire at the point of interest.

## 3. What factors affect tension T in a parabolic wire?

The tension T in a parabolic wire is affected by the mass of the wire, the acceleration due to gravity, the length of the wire, and the height of the wire at the point of interest. Additionally, the material and thickness of the wire can also affect tension.

## 4. How does tension T change at different points along a parabolic wire?

Tension T in a parabolic wire is highest at the lowest point of the curve, and decreases as you move towards the ends of the wire. This is because the weight of the wire is distributed more evenly at the ends, compared to the concentrated weight at the lowest point.

## 5. What is the practical application of understanding tension T in a parabolic wire?

Understanding tension T in a parabolic wire is important in engineering and construction, as it helps determine the strength and stability of structures that use parabolic wires. It can also be used in other fields such as physics and mathematics to study the properties of curves and forces.

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