ME 201Engineering Mechanics: Statics

Chapter 3 – Part A3.1 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 Object at rest

Then to satisfy Newton’s first law, the resultant force acting on a particle is zero, or

0 F

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

Active forces Reactive forces

Label known forces proper magnitude & direction Watch signs

Negative answer means opposite in sense from FBD

Free Body DiagramExample

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)