1. Equilibrium of a particle
Chapter 3
Equilibrium of a particle

2.  F = ma = 0 1. Equilibrium F2 F1 F3 F = 0
3-1 Condition for the Equilibrium of a particle
1. Equilibrium
A particle is in equilibrium provided it is at rest if originally
at rest and in motion if originally moving at constant velocity.
2. Necessary & Sufficient condition F1 F2 F3
Newton’s first law of motion.
F = 0
Newton’s second law of motion
 F = ma = 0
a = 0 = d V / d t
V = Constant

3. 3-2 Free-Body Diagram 1.Definition of FBD
A FBD is a sketch of the particle ,which shows the particle”free”
from its surroundings with all the forces that act on it.
2.Connections F
(1) Spring k
Linear elastic spring.
Hooke’s Law: F=KS S
K:spring constant or stiffness.
S:stretch of spring.
If S(+) => F pulls the spring
S(-) => F pushes the spring
(2) Cables & pulleys
a. Negligible Weight, cannot be stretched T’
b. Support only a tension or pulling force T
c. constant tension throughout its length . T=T’

4. a. Force tends to set the particle in motion.
3.Forces
(1) Active Force
a. Force tends to set the particle in motion.
b. Forces caused by attached cables, weight, or magnetic and
electrostatic interaction.
(2) Reactive Force
Forces caused by the constraints or supports tending to prevent
motion .
Example
FBD of the ring at A W A B C
Ta=W Tb Tc

5. 3-3 Coplanar Fore Systems ( 2 D )
1. Particle equilibrium F2 F1 F3 Fn
F1 , F2, F3, …Fn
Coplanar force in x y plane.
Equations of Equilibrium
F = 0
In Cartesian vector form
F = Fx + Fy
= Fx i + Fy j = 0
Scalar equilibrium equations
Fx = Fy = 0

6. 2. Procedure for analysis
(1) Draw Free-Body Diagram
(a) Establish the x y axes
(b) Label all forces
(2) Apply equations of equilibrium
(a) Fx = 0
Fy = 0
(b) Fs = k s
if more than two unknowns exists and a spring involves.

7. 3-4 Three-Dimensional Force Systems
F Z F2 Y F4 F1 X
1. Particle equilibrium in 3D
Hence equation of equilibrium is
F = 0
In Cartesian Vector form
Fxi + Fyj + Fz = 0 So
Fx = Fy = 0
Fz = 0
2. Analysis Procedures
Same as sec. 3.3.