Engineering Statics Equilibrium System Question

In summary, the conversation discusses a solution to a physics problem involving a system with a horizontal force, a perpendicular force, and weight. The individual explains their approach and equations used, ultimately arriving at an answer of θ = cos^-1 ( (2a/L) ^(1/3) ). They express doubt about their answer, but another participant points out that it is consistent with the units and changing W would affect the units.
  • #1
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Homework Statement


http://i.imgur.com/VFb5rwj.png


Homework Equations





The Attempt at a Solution


First, I drew the FBD for the system, one horizontal force at A, one force perpendicular to the beam at B, and the weight.
Writing out the equilibrium equations:
The sum of forces in the y direction should be 0, so I have the equation:
Nb cos(θ) - W = 0, which can be rearranged for Nb later on.
Then I took the moment about point A:
Nb (a/cosθ) - Wcosθ (L/2) = 0
Eventually, it simplifies out to cos^-1 ( (2a/L) ^(1/3) ) = θ

I don't think I got the right answer, but can someone help me identify my error? Thank you in advance.
 
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  • #2
Why do you think you have the wrong answer?
 
  • #3
IDK, it looks just so completely wrong. and also it says that describe it in terms of w, a, and l and I have no w.
 
  • #4
Would changing W also change θ?

Also your answer is consistent with the units. If W was in the solution then the units would get screwed up.
 
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  • #5
Hmm, I suppose you're right, thank you for the replies.
 

FAQ: Engineering Statics Equilibrium System Question

1. What is the definition of static equilibrium in engineering?

Static equilibrium in engineering is a state in which all external forces acting on a system are balanced and the system is at rest or moving at a constant velocity. This means that there is no acceleration in any direction and the system is in a state of balance.

2. What are the key principles of static equilibrium in engineering?

The key principles of static equilibrium in engineering are:

  • Newton's First Law of Motion: an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity unless acted upon by an external force.
  • Newton's Second Law of Motion: the sum of the forces acting on an object is equal to the mass of the object multiplied by its acceleration (F=ma).
  • Newton's Third Law of Motion: for every action, there is an equal and opposite reaction.

3. How do you determine if a system is in static equilibrium?

To determine if a system is in static equilibrium, you must first draw a free body diagram and identify all the external forces acting on the system. Then, using the principles of static equilibrium, you can set up equations to find the net force and net torque acting on the system. If the net force and net torque are both equal to zero, then the system is in static equilibrium.

4. What are some real-life applications of static equilibrium in engineering?

Static equilibrium is used in many real-life applications, such as:

  • Designing bridges and buildings to ensure they can withstand external forces without collapsing.
  • Calculating the forces acting on a plane during flight to maintain its position and stability.
  • Determining the weight distribution and stability of a vehicle to prevent tipping over.
  • Designing support structures for heavy machinery to prevent them from toppling over.

5. What are the limitations of static equilibrium in engineering?

While static equilibrium is a useful concept in engineering, it does have some limitations. These include:

  • It only applies to systems that are at rest or moving at a constant velocity. It cannot be applied to systems with acceleration.
  • It assumes that all forces are acting in a single plane and do not change direction.
  • It does not take into account the effects of friction, which can play a significant role in real-life systems.
  • It is a simplified model and may not accurately represent complex real-world systems.

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