Boom held by 3 cables (Statics)

In summary, the problem asks for the tension in a cable when two cables are attached to a boom. The attempt at a solution is to resolve the tensions exerted at points A and D on the boom, and then use the resultant force to determine the tension in the cable. If the sum of the cable forces is directed along AB, the force in the boom is also directed along AB. So if you take moments about a point on the line AB, the unknown force in the boom (which you are not asked to find) has zero moment. Point B will do nicely.
  • #1
masterflex
17
0

Homework Statement


I've included a picture of the problem so you can see the diagram too. The question is asking for the tension of 1 cable, when 2 are given (problem# 41).

Homework Equations


no equations per se.

The Attempt at a Solution


I resolved cable AC and cable AD, but don't know how to proceed. How do you even analyze it with the given info that "the resultant of the tensions exerted at point A of the boom must be directed along AB"? This is hard. Thanks for helping me.
 

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  • #2
Seems like if the sum of the torques were zero, that would satisfy the situation. Is that enough to figure it out? (I don't know offhand)
 
  • #3
berkeman said:
Seems like if the sum of the torques were zero, that would satisfy the situation. Is that enough to figure it out? (I don't know offhand)

If the sum of the cable forces is directed along AB, the force in the boom is also directed along AB.

So if you take moments about a point on the line AB, the unknown force in the boom (which you are not asked to find) has zero moment. Point B will do nicely.

Hint: first work out the angle between each cable and the boom AB, then taking the moments is easy.
 
  • #4
I understand

Thanks a lot for your help guys. I got this solution from a random professor that I just walked in the door to talk to. I also realized what I was struggling with: there's a force along the line of AB (but not necessarily constrained to that physical distance; just in line with it), but I didn't know what to make of that force even though the problem said it was there. One easy way to know how many forces are in play at any given point is to look at the number of things (booms, cables, hanging things, whatever).

The moment solution should work -- I mean it sounds good :D, and I'll give it a try. Thanks for that.

By the way, the prof approached this like an equilibrium problem just using plane forces. I've attached my work.
 

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1. What is the purpose of using 3 cables to hold a boom?

The purpose of using 3 cables to hold a boom is to provide stability and support for the boom. By using multiple cables, the load on each individual cable is reduced, making it less likely for the cables to fail or break under the weight of the boom.

2. How do you determine the tension in each cable?

The tension in each cable can be determined using the principles of statics, specifically the equations of equilibrium. By considering the forces acting on the boom and the cables, the tension in each cable can be calculated using the equations of Newton's second law and the summation of forces in the x and y directions.

3. What factors affect the stability of a boom held by 3 cables?

There are several factors that can affect the stability of a boom held by 3 cables, including the weight and length of the boom, the angle of the cables, and the tension in each cable. Additionally, external factors such as wind and other loads acting on the boom can also affect its stability.

4. How do you ensure that the boom and cables do not fail under the load?

To ensure that the boom and cables do not fail under the load, it is important to calculate and distribute the tension in each cable evenly. This can be achieved by properly adjusting the length and angle of the cables and ensuring that the load is evenly distributed along the boom. Additionally, regular maintenance and inspection of the boom and cables can help identify any potential issues before they become a safety hazard.

5. Can the 3-cable system be used for any type of boom?

The 3-cable system can be used for a wide range of boom types, including cranes, construction equipment, and even flagpoles. However, the design and specifications of the cables may vary depending on the weight and length of the boom, as well as the intended use and load capacity of the boom. It is important to consult with a structural engineer or follow manufacturer guidelines to ensure the 3-cable system is appropriate for the specific boom being used.

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