1. Equilibrium
& supports

2. Equilibrium of a particle:
A particle is said to be in equilibrium if it remains at
rest.
Or has constant velocity if originally in motion most
often.
How ever the term of "equilibrium" or more specifically
"static equilibrium" is used to describe the things at
rest.
It is necessary to satisfy Newton's first law of motion.
∑F = 0
Where F is a vector.

3. Coplanar forces:
If the particle lays on X-Y plane.
The each forces can be solved into I & J for equilibrium.
F1 cos θ – F2 cos φ = 0
F1 sin θ + F2 sin φ = 0

4. Equilibrium of rigid body:
We can develop the both necessary and sufficient
condition for equilibrium.
This body is subjected to force, couple and moment
system.
This is the resultant of gravitational force, electric,
magnetic or contact forces caused by adjacent
bodies.
The internal forces caused by inter action between
particles can't be seen in figure and equal but
opposite.
So, we cancel it.

5. Supports in two dimension:-
*Pins

6. *Roller

7. •Cable and link

8. •Smooth surface

9. •Rough surface

10. •Fixed support

11. Where,
F: is the force exerted by the spring
K: is spring constant
: the length of spring after elongation
: the original length before elongation
. The force exerted by spring

12. . Free body diagram
It is a successful application of equation
of equilibrium require complete specificant
of all known and unknown external force
that acts on the body , the best way for this
to draw the free body diagram.
It is necessary to draw all forces and couple
on it.

13. Example(1): In the shown figure. Determine the tensions in 3
cables
(Given: m=60Kg,tanθ=
)

14. The equations of equilibrium:
(1)
(2)
Solving (1)&(2):

15. Example(2):

16. Example(3):
N

17. References :
1/ Engineering mechanics statics by
R. C. HIBBELER
2/ Lecture notes annotated by
Dr . Mohamed tawfik
Cairo university
Assistant Professor
Giza, Al Jizah, Egypt