Wize University Statics Textbook (Master) > Equilibrium of a Particle

A Free-Body or Force-Body Diagram (FBD) allows you to isolate the object of interest, and observe the forces acting on it.  It's a sketch which shows the body FREE from its surroundings with ALL KNOWN & UNKNOWN forces acting on it.

STEP 1: construct a FBD
Decide what you’re interested in, and draw a diagram of it
     2.  Draw and label all forces acting on the body, and indicate angles where necessary
If you don't know the force, use F.
If you don’t know the direction of a force, assume a direction.  If force answer is negative, then the force acts in the opposite direction.  Exaggerate the angles if it helps
 You must account for ALL KNOWN & UNKNOWN forces acting on the particle/body
     3.  Include W (Fgravity=weight=mg), where applicable

     4.  Define a coordinate system
          a.  This can be the general xy (2D) or xyz (3D) coordinate system you’re used to
          b.  Or it could be a rotated coordinate system that simplifies the problem (helpful when analyzing objects on an inclined plane, like in problems involving friction)
          c.  LABEL axes, indicating the "+" direction.

***Drawing a FBD is required for every question (where applicable)***
(besides being required, IT IS A GOOD PLACE TO START!!!!)


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STEP 2: choose equations

The next step would be to sum forces to be equal to a resultant force. If the system is at equilibrium, then the resultant force is zero.

When setting up equations, remember:

Number of Unknowns=Number ofEquationsNEEDEDNumber\ of\ Unknowns = Number\ ofEquations NEEDEDNumber of Unknowns=Number ofEquationsNEEDED

Where to get that many equations:
Begin by using equations of equilibrium (sum F's in x, y, and z (if 3D)) 
(in the next section we will add sum M's about the x, y, and z axes (in 3D) to this list
Use spring equations where applicable
Use geometric equation if necessary

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You learned how to draw a FBD for particles, and now it’s more important to know how to draw FBDs for bodies. The steps are essentially the same, but remember to account for moments, and include a coordinate system if one isn't provided for you.

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Lets Practice!
1) Draw FBD for point B. 


2) Draw FBD for Point A. 
3)
-Draw FBD for the beam.
-Draw FBD for the pulley system isolated (point C). 


A good guideline to setting up equations is

Number ofEquations=Number of UnknownsNumber\ ofEquations=Number\ of\ UnknownsNumber ofEquations=Number of Unknowns
To get that many equations:
Begin by using equations of equilibrium
Use spring equations where applicable
Use geometric equation if necessary
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The lamp weights 57 N. Determine the tension in each of AB and AC needed to carry the lamp.

Tension of AB is ___ newtons.

Answer

I don't know

Determine the maximum allowable weight for the lamp at F if each of the cables can only handle a load of 50 N. 

Answer

I don't know