Can the tension in a hanging cable be determined with known length and location?

In summary, the conversation discusses determining the tension a in the equation of a hanging cable with known length and end points. The equation involves a horizontal translation h and the weight of the cable is not important for a computer simulation. It is possible to find a numerical approximation for a based on the given information and an equation involving the distance between end points and the length of the cable. There is also a question about whether this method would work for end points of unequal height and if the equation used is correct for this type of catenary. Lastly, there is a question about solving for tension in a scenario where the force acting on the cable is not equally distributed, such as a fish on a fishing rod or a cable with increasing density towards one end
  • #1
joel_f
2
0
hi~
i need to determine the tension a in the equation of the hanging cable y=acosh(x-h)/a+k with a known length and known location of end points. i figured out how to determine the horizontal translation h but i need a in order to do it and to have the complete equation.

this is for a computer simulation where the weight of the cable is not important. this is why i condensed tension in the formula down to a. if the weight is a requirement then it can be set, in which case i would need to find the horizontal force acting on the cable.

is it possible to find the tension with the given information?
 
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  • #2
The length of the cable L is given by [tex]y=2a\mbox{sinh}\left(\frac{d}{2a}\right)[/tex], where d is the distance between the end points of the cable (I assumed they were at equal heights based on your equation). You can get a numerical approximation of a from this equation after substituting in the known values of d and L.
 
  • #3
would this work for end points of unequal height? am i using the wrong equation for the catenary of this type?
 
  • #5
Hello benorin,

I hope you will still get this. I very much liked your extensive answer of the problem.

What if you would replace the force acting on the cable from being gravity to drag. In other words what if the force is not equally distributed. Like a fish on a fishingrod swimming around the fisherman, or a cable with increasing density towards one end.

Can this be solved?

Regards,
Seuren
 

What is a hanging cable (catenary)?

A hanging cable, also known as a catenary, is a curve that is created when a cable or chain is hung between two points. The weight of the cable causes it to take the shape of a curve, with the lowest point being directly below the two points of support.

What is the significance of a hanging cable (catenary)?

Hanging cables have many practical applications, including supporting bridges and suspension systems, as well as being used in mathematical and scientific calculations. The shape of a hanging cable is also used in architecture and design to create aesthetically pleasing structures.

How is the shape of a hanging cable (catenary) determined?

The shape of a hanging cable is determined by the weight of the cable and the tension applied at the two points of support. The curve is known as a catenary and is a hyperbolic cosine function.

What factors can affect the shape of a hanging cable (catenary)?

The shape of a hanging cable is affected by the weight of the cable, the tension applied at the two points of support, and the distance between the two points. Other factors such as wind, temperature, and other external forces can also affect the shape of a hanging cable.

How is a hanging cable (catenary) different from a parabola?

While a hanging cable and a parabola may appear similar in shape, they are different curves with different equations. The shape of a hanging cable is determined by its weight and tension, whereas a parabola is a symmetrical curve that is defined by a quadratic equation.

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