Equilibrium& supports

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 = 0Where F is a vector.

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

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.

Supports in two dimension:-

*Pins

*Roller

•Cable and link

•Smooth surface

•Rough surface

•Fixed support

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

. 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.

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

)

The equations of equilibrium:

(1)

(2)

Solving (1)&(2):

Example(2):

Example(3):

N

References: 1 /Engineering mechanics

statics by R. C. HIBBELER2 /Lecture notes annotated by

Dr . Mohamed tawfik Cairo university

Assistant Professor, Giza , Al Jizah Egypt