# How to Find the Tension in a Cable

To find the tension in a cable, consider a symmetrical hanging of a sign. The sign weighs five kilograms, and a 100-degree angle exists between the two cables. If gravity pulls the weight down, the two cables must exert an equal amount of upward force to balance the weight. This requires each cable to exert a 24.5 N force to pull upward. Therefore, the total tension in each cable is two times the force applied by gravity.

## Calculating tension

If you are working on a cable system, you must calculate the tension in each of the cables. There are a couple of methods to calculate this. First, you can use a force equation based on frequency. This method is the most popular and has a good track record. Then, you can use a different force equation based on the length, model number, and natural frequency of the cable. Alternatively, you can attach accelerometers to individual cables.

Another method is to measure the tension force by determining the peak tension force of each cable in the system. In this case, the weight of the crossing vehicle is assumed to be the central value. Once you calculate this force, you can estimate the stress amplitudes of individual cables. This method has the advantage of being simple to use and accurate. This method is also known as the force-time-frequency-interaction method.

Another method is to use trigonometry. You can also use free-body diagrams to determine tensions. For example, you can use a triangle to calculate the tension in one cable. It is important to note that the angle between the horizontal and the angle of the free body must be equal to calculate the tension. If there are two cables with equal lengths, they cancel each other out. This method requires you to know the angle of each cable before you can calculate the tension in the other cable.

## Using trigonometric functions

Consider the weight of a picture hanging on a wall. If the picture has a mass of 10 kg, the tension in the diagonal cable would be ten times the mass of the sign. Similarly, the mass of a sign hanging outside a physics classroom is 50 kg. By using trigonometric functions, you can calculate the tension in the diagonal cable.

Consider a situation where you want to hang a 10-Newton picture. If the two cables are attached to each other by three wires that each support half of that weight, you’ll need to determine the tension t in each cable using trigonometric functions. Then, you’ll know how much tension each cable must exert in order to hold the sign.

First, measure the angle of the vector from the positive x-direction. Then, calculate the angle of TL in the opposite direction, which is 37deg. Using this equation, you’ll see that the x-component of 1 is negative, while the y-component of the second wire is positive. These two measurements are equal, and the forces are equivalent.

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## Using a sketch to assist with the solution

A sketch is a graphical representation of a problem that is used to solve it. Sketches can be used to create geometric constraints on an object by using the Constrained Tool. When constraints are applied to a sketch, it stabilizes the shape and position of the object and allows predictable editing. For example, dragging the endpoint of a constrained line will not change its perpendicularity. A sketch can be fully constrained or partially constrained. A sketch’s degree of freedom can be displayed using the ‘Degrees of Freedom’ glyph.

After creating the Sketch Board, post it on a wall to get feedback from colleagues. Alternatively, upload it to a collaborative online platform such as FigJam or Mural. Use different techniques such as “Dot voting”, “Speed critique,” or “Supervote” to encourage your team members to give you feedback on your sketch. Focus on the parts of your sketch that are interesting to you. Create alternatives for those parts that are not.

A sketch can help you communicate design decisions more effectively and explore design space. It can help you avoid suboptimal design choices and keep your design objective in focus. Sketches can also be a good way to capture ideas that may otherwise go unnoticed. You can capture the ideas and designs of others in your sketchbook, or you can use them to inspire yourself to do the same. Once you have collected several sketches, it’s time to put them to use in your own creative work.