Static Equilibrium: A 1380 N uniform boom of length ℓ is supported by a cable

In summary, the question is asking to find the tension in the cable supporting a 1380 N uniform boom with a 3604 N weight hanging from it. The boom is pivoted at the bottom and the cable is attached 3/4 of the way up the boom. Using the sum of torques in the system, a solvable system of equations can be found to determine the tension of the cable. The total length of the boom is given as L.
  • #1
sb42
3
0

Homework Statement



A 1380 N uniform boom of length ℓ is supported by a cable, as shown. The boom is pivoted at the bottom, the cable is attached a distance 3/4ℓ from the pivot, and a 3604N weight hangs from the boom’s top. Find the tension of the cable.

here is a picture of the diagram
24.media.tumblr(dot)com/tumblr_m3f8sxRH7H1qdg2z1o1_400.jpg[/PLAIN]

Homework Equations



I know that the sum of the forces in the x direction is 0 and the sum of the forces in the y direction is also 0. I am having issues understanding this concept and I don't understand how to even start this.

The Attempt at a Solution



Ive tried buy getting the forces in the x and y direction but it seems as though I should be able to find the tension of the cable without finding these first. One thing that is throwing me off is the fact they don't give and actual length to the rod.
Any help would be appreciated!
 
Last edited:
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  • #2
What is the actual question? Find the tension in the cable?
 
  • #3
Yes, sorry forgot to paste that bit.
 
  • #4
You should be able to find it fairly easily if you sum of the torques in the system. This should give you a solvable system of equations. They give you the length of the rod, it's total length is L.
 
  • #5
Thank you!
 

FAQ: Static Equilibrium: A 1380 N uniform boom of length ℓ is supported by a cable

1. What is static equilibrium?

Static equilibrium refers to a state in which all forces acting on an object are balanced, resulting in no net movement or acceleration.

2. How is static equilibrium achieved?

In order for an object to be in static equilibrium, the sum of all the forces acting on the object must be equal to zero. This can be achieved by either having all the forces cancel each other out (i.e. equal and opposite forces), or by having the object at rest with no external forces acting on it.

3. What is the significance of a 1380 N uniform boom?

The 1380 N refers to the weight or force of the boom, which is the force that is being supported by the cable. A uniform boom means that the mass or weight is evenly distributed along the length of the boom.

4. How is the cable supporting the boom?

The cable is supporting the boom by exerting an upward force equal to the weight of the boom (1380 N). This is known as tension force and it keeps the boom in place and prevents it from falling down.

5. Why is the length of the boom important?

The length of the boom is important because it affects the amount of torque (rotational force) exerted on the cable. The longer the boom, the greater the torque, and the higher the tension force needed to keep the boom in static equilibrium. This is why longer booms may require thicker or stronger cables for support.

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