1. 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

2. Key Concepts  Equilibrium of a Particle  Free Body Diagrams  Problem Solving Methodologies

3. 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 Object at rest  Then to satisfy Newton’s first law, the resultant force acting on a particle is zero, or

4. Equilibrium of a Particle In vector notation: ∑ F x i + ∑ F y j = 0 Or, for this equation to be satisfied ∑ F x = 0 ∑ F y = 0

5. 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)

6. Creating a Free Body Diagram  Sketch the isolated particle (or member…)  Sketch all forces that act on the particle Active forces Reactive forces  Label known forces proper magnitude & direction  Watch signs Negative answer means opposite in sense from FBD

7. Free Body Diagram Example

8. 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  Active forces  Reactive forces  Label known forces with proper magnitude & direction  Watch signs – negative means opposite sense from as drawn in FBD 2.Apply equations of equilibrium  Any suitable direction  2 equations, 2 unknowns (n equations, n unknowns)