ME 201
Engineering Mechanics: Statics
Chapter 3 – Part A
3.1 Condition for the Equilibrium of a Particle
3.2 The Free-Body Diagram
3.3 Co-Planar Force Systems
Key Concepts
 Equilibrium of a Particle
 Free Body Diagrams
 Problem Solving Methodologies
Equilibrium of a Particle
 A particle is in equilibrium provided it is at rest if
originally at rest, or has a constant velocity if
originally in motion
 Static equilibrium
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Object at rest
 Then to satisfy Newton’s first law, the resultant
force acting on a particle is zero, or
F  0
Equilibrium of a Particle
In vector notation:
∑ Fxi + ∑ Fyj = 0
Or, for this equation to be satisfied
∑ Fx = 0
∑ Fy = 0
Free Body Diagrams
 A Free Body diagram is a simple sketch of
the particle (or member), including all forces
that act on the particle (or member)
Creating a Free Body Diagram
 Sketch the isolated particle (or member…)
 Sketch all forces that act on the particle
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Active forces
Reactive forces
 Label known forces proper magnitude & direction
 Watch signs
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Negative answer means opposite in sense from FBD
Free Body Diagram
Example
Steps to Problem Solving
1.
Draw a Free Body Diagram (FBD), label known and
unknowns
Simple sketch of isolated particle
Sketch all forces that act on the particle
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2.
Active forces
Reactive forces
Label known forces with proper magnitude & direction
Watch signs – negative means opposite sense from as drawn in
FBD
Apply equations of equilibrium
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Any suitable direction
2 equations, 2 unknowns (n equations, n unknowns)