Angle between catenary and line

In summary, to find the angle between the line x=7 and the catenary y=20\cosh{(\frac{x}{20})}-15, you can use the formula tan^{-1}(\frac{1}{sinh(7/20)}) and evaluate it using a calculator or find a numerical solution.
  • #1
flash
68
0

Homework Statement


Find the angle between the line x=7 and the catenary [tex]y=20\cosh{(\frac{x}{20})}-15[/tex]

The Attempt at a Solution



I found the tangent has gradient [tex]\sinh{(\frac{7}{20})}[/tex]

Then I used [tex]\tan{\theta}=|\frac{1}{m}|[/tex]
where [tex]m=\sinh{(\frac{7}{20})}[/tex]

And evaluated using inverse tan on my calculator.

I'm pretty sure we aren't meant to use a calculator though, so my question is can the inverse tan of that be evaluated manually somehow?

Thanks
 
Physics news on Phys.org
  • #2
If you "aren't meant to use a calculator" then give, as your answer,
[tex]tan^{-1}(\frac{1}{sinh(7/20)})[/tex]
There is no simple way to calculate a numerical solution.
 

1. What is the angle between a catenary and a line?

The angle between a catenary and a line is constantly changing and depends on the specific points on the curve and line being considered. Therefore, it is not possible to give a single definitive answer to this question.

2. How does the angle between a catenary and a line affect structural stability?

The angle between a catenary and a line can affect the structural stability of a hanging cable or bridge. Generally, a smaller angle will result in more tension being placed on the cable, while a larger angle may result in more compression. However, the exact effects on stability will depend on the specific design and materials used.

3. Can the angle between a catenary and a line be calculated?

Yes, the angle between a catenary and a line can be calculated using mathematical equations and techniques. However, these calculations can be complex and may require specialized knowledge and tools.

4. How does the catenary equation calculate the angle between a catenary and a line?

The catenary equation, which describes the shape of a hanging cable, can be used to calculate the angle between a catenary and a line at a specific point. This is done by taking the derivative of the catenary equation and solving for the angle at that point.

5. Are there real-world applications for understanding the angle between a catenary and a line?

Yes, understanding the angle between a catenary and a line is crucial in the design and construction of structures like suspension bridges and power lines. It can also be useful in fields such as architecture and engineering, where knowledge of the angle can help ensure the stability and safety of various structures.

Similar threads

  • Calculus and Beyond Homework Help
Replies
2
Views
564
  • Calculus and Beyond Homework Help
Replies
1
Views
787
  • Classical Physics
Replies
17
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
488
  • Mechanics
Replies
2
Views
216
  • Advanced Physics Homework Help
Replies
4
Views
305
  • Calculus and Beyond Homework Help
Replies
2
Views
978
  • Calculus and Beyond Homework Help
Replies
2
Views
5K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
Back
Top