1. ES2501: Statics/Unit 6-1: Equilibrium of Particles (2D cases)
Equilibrium Equations:
Equilibrium
Resultant
force
For ANY given
direction
Vector
form
For a Cartesian
System given 2D
Case
Total projection in
ANY given direction
is zero
1D Case
Scalar
form

2. ES2501: Statics/Unit 6-2: Equilibrium of Particles (2D cases)
General Conclusions:
For each particle there is ONE vector equilibrium equation, which
is equivalent to THREE scalar equations for 3D problems, TWO
scalar equations for 2D problems, and ONE scalar equations for
1D problems.
If there are more unknowns than the number of scalar equilibrium
equations it is a STATICALLY UNDERMINATED problem, for
which some supplementary equations are needed for solution
If two forces are in equilibrium, they are collinear;
If three forces are in equilibrium, they are coplanar
If three forces are in equilibrium
For three forces ONLY
Equivalent but more
convenient

3. ES2501: Statics/Unit 6-3: Equilibrium of Particles (2D cases)
Example 1: Find
tensions of cables
Note: Sign
convention
Step 1: Free-Body Diagram
Step 2: List Eqs
FBD of point C
Action and
reaction
Staticaly determinant vs
statically underminant
problems
FBD of block
Step 3: Solution
three eqs for
three unknowns
Alternative Solution:

4. ES2501: Statics/Unit 6-4: Equilibrium of Particles (2D cases)
Example 2: Find the friction
between block A and the slope
And tension in the cable
Step 1: Free-Body Diagram
FBD of A
Step 2: List Eqs
FBD of A
three eqs for
three unknowns
Direction of friction
is uncertain depending
on tendancy of motion
Upwards or downwards
Step 3: Solution