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STATIC EQUILIBRIUM
An object is said to be in static equilibrium if it is moving at constant velocity, or it is simply at rest, that is, not moving, rotating or translating. Note that this stationary object/mass can be acted on by several forces; however, the net forces must equal to zero in order to satisfy the no translation condition or constant velocity condition. In order to guarantee static equilibrium not only do the net forces must equal to zero but so do the net moments. Think about the case of a rod with two equal but opposite forces acting at each end of the pole. Here the net forces from the couple is equal to zero, but the net moments do not. This will cause the rod to rotate and thus it is not in static equilibrium.
SOLVING A PROBLEM
The net forces and moments for an object in static equilibrium are given in the equilibrium equations as follows:
Equilibrium Equations
ΣFx = 0
ΣFy = 0
ΣMp = 0
It is important to know where to begin when solving a statics problem. By following the next few guidelines one should be able to figure out just about every statics problem out there.
1. Identify and draw an coordinate system that suits your needs
Note: It is important to understand that one should never switch coordinate systems while solving a problem. Pick one, and be consistent.
2. Identify the force vectors and objects of interest.
3. Draw a free body diagram.
4. Use the various angle relationships to identify the necessary angles.
5. Draw a right triangle for each force.
Note: Remember to use the hypotenuse as the force
6. Apply the equations of equilibrium (Newtons 2nd law set to zero)
7. Designate any point on the body to take moments about