What is the equation for solving static equilibrium questions?

In summary: So set the forces equal to each other and solve for the missing variable.In summary, for solving static equilibrium questions involving beams supported by cables, you need to make the torque provided by the cable equal to the torque caused by the weight of the beam. This can be done by setting the perpendicular components of the torques equal to each other and solving for the missing variable. For the second question, the horizontal component of the cable's force can be used to determine the force that the pin must provide to keep the beam in equilibrium.
  • #1
XodoX
203
0
I do not understand how to solve static equilibrium questions. Like those:

The figure shows a uniform, horizontal beam (length = 10 m, mass = 25 kg) that is
pivoted at the wall, with its far end supported by a cable that makes an angle of 51o with
the horizontal.(mass = 60 kg) stands 3.0 m from the pivot, what is the tension in the
cable?

Or this one

http://www.chegg.com/homework-help/questions-and-answers/a-uniform-120-lb-beam-is-supported-in-a-horizontal-positionby-a-pin-and-cable-as-shown-in--q701621

The second one with the pin is especially hard, imo.

I don't even know what the basic equation here is. The book dosen't tell you this. It's always [itex]\Sigma[/itex][itex]\tau[/itex]=... something else. So I do have to create my own equation each time, basically. Is this correct? Depending on whatever the problem is. I don't get it. Can someone please explain this to me?
 
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  • #2
For these types of questions, essentially you make the torque provided by the cable equal to the torque caused by the weight of the beam. This must be true, because otherwise the beam would be rotating on its pivot. I can't really help you with anything until you show me an attempt at a solution.
 
  • #3
tal444 said:
For these types of questions, essentially you make the torque provided by the cable equal to the torque caused by the weight of the beam. This must be true, because otherwise the beam would be rotating on its pivot. I can't really help you with anything until you show me an attempt at a solution.

I already have the solution... that's not my question. I'm wanting to know how to solve those kind of problems/concepts.
 
  • #4
I essentially just told you in my last post. Think of torque as acting either clockwise or counterclockwise about the pivot. Take the perpendicular components and make them equal each other. Solve for missing variable. If you're looking for a basic equation, there isn't really one. All torque questions are based off the fact that the sum of torques must be equal to zero.
 
  • #5
tal444 said:
I essentially just told you in my last post. Think of torque as acting either clockwise or counterclockwise about the pivot. Take the perpendicular components and make them equal each other. Solve for missing variable. If you're looking for a basic equation, there isn't really one. All torque questions are based off the fact that the sum of torques must be equal to zero.

What are the perpendicular components for the 1st example? Torque(0)=Tsin51*length of beam -weight of person*meters from the pivot - weight of beam*(I don't know). Don't know what the last component in this equation would be. But then I would solve it for T. I have no idea if this equation would get me the tension of the cable., but that's what I can come up with.
 
  • #6
You've got it mostly right. The beam's center of gravity is in the middle, so how far away from the pivot is it acting on?
 
  • #7
Well, since it's in the middle, it's 5m.
 
  • #8
Yes. With that information, you should be able to solve for T.
 
  • #9
But that is the tension of the cable. How would I do the second one? How do I know how to approach this ?
 
  • #10
For the second question, the cable is acting at an angle right? This means that the cable has a horizontal force. Since the beam is not moving, therefore the pin must be supplying a horizontal force that either pushes out against the beam or pulls it toward the wall to stop it from moving sideways.
 
  • #11
tal444 said:
For the second question, the cable is acting at an angle right? This means that the cable has a horizontal force. Since the beam is not moving, therefore the pin must be supplying a horizontal force that either pushes out against the beam or pulls it toward the wall to stop it from moving sideways.

I don't think I fully understand this, but would it look like this?

Basically the same I did above but just for this problem?
 
  • #12
Find the horizontal component of the force that the cable is pulling on the beam. The force that the pin provides will be equal to that.
 

1. What is static equilibrium?

Static equilibrium refers to the state of an object when all forces acting upon it are balanced and there is no net change in its motion.

2. How do you determine if an object is in static equilibrium?

An object is in static equilibrium if the sum of all forces acting upon it is equal to zero and the sum of all torques acting upon it is also equal to zero.

3. What is the difference between static and dynamic equilibrium?

In static equilibrium, the object is at rest or moving at a constant velocity, while in dynamic equilibrium, the object is moving at a constant velocity with changing direction.

4. Can an object be in static equilibrium if it is moving?

No, an object cannot be in static equilibrium if it is moving. Static equilibrium requires that there is no net change in an object's motion, meaning that the object must be at rest or moving at a constant velocity.

5. How do you solve static equilibrium problems?

To solve static equilibrium problems, you must first identify all the forces acting upon the object and their respective directions. Then, you can use Newton's first law, which states that the sum of all forces must equal zero, and the sum of all torques must also equal zero. From there, you can set up and solve equations to find the unknown variables.

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