Transcript EQUILLIBRIUM

EQUILLIBRIUM
BY
GP CAPT NC CHATTOPADHYAY
MEANING
• Latin aequilībrium, equivalent to aequiequi- + lībr ( a ) balance + -ium –ium
• -ium: a suffix found on nouns borrowed
from Latin, especially derivatives of verb
• Synonyms
equipoise, steadiness, stability.
DEFINITION
• Condition in which the net force / and
moment acting on a particle is zero. A body in
equilibrium experiences no acceleration and,
unless disturbed by an outside force
/moment, will remain in equilibrium
indefinitely.
AFTER A LOT OF STUDIES……
EXAMPLE OF
EQOUILLIBRIUM
TYPES
• A STABLE EQUILIBRIUM IS ONE IN WHICH SMALL, EXTERNALLY INDUCED
DISPLACEMENTS FROM THAT STATE PRODUCE FORCES THAT TEND TO OPPOSE
THE DISPLACEMENT AND RETURN THE BODY TO EQUILIBRIUM
• AN UNSTABLE EQUILIBRIUM IS ONE IN WHICH THE LEAST DEPARTURES PRODUCE
FORCES TENDING TO INCREASE THE DISPLACEMENT.
• IN NEUTRAL EQUILLIBRIUM A BODY IF DISTURBED CHANGES IT’S POSITION AND
THEN STEADY. EVERY TIME A NEW POSITION IS ADOPTED
• A BALL IN A CUP IS IN STABLE EQUILIBRIUM
• BRICK LYING ON THE FLOOR IS IN NEUTRAL EQUILIBRIUM
• A BALL ON AN INVERTED CURVED SURFACE IS IN UNSTABLE EQUILIBRIUM
EXAMPLES
REAL TIME SITUATIONS
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BODY IS IN MOTION
N, τ, V’ ?
BODY IS IN ROTATION
N, τ, V’ ?
COMBINED ACTION OF MOTION AND ROTATION
BODY IS AT REST
N, τ, V ALL ZERO
CONDITIONS
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MOTION- ∑F = 0
ROTATION- ∑M = 0
COMBINED ACTION - ∑F = 0, ∑M = 0
REST - ∑F = 0, ∑M = 0
CONDITIONS ..CONTD….
• As applied to a rigid body, the necessary and
sufficient conditions become:
“A rigid body is in mechanical equilibrium
when the sum of all forces on all particles of the
system is zero, and also the sum of all Moments
on all particles of the system is zero. “
A rigid body in mechanical equilibrium is
undergoing neither linear nor rotational
acceleration; however it could be translating or
rotating at a constant velocity.
COMPLEX BODY
COMPLEX STRUCTURES POSE DIFFICULTY IN ANALYSIS
SOLUTION ?
• FREE BODY CONCEPT
• FREE BODY IS AN ISOLATED BODY SEPARATED
FROM THE COMPLEX PARTS REPRESENTING
ALL FORCES INCLUDING REACTIONS AND
MOMENTS IT EXPERIENCES
• IT HELPS IN SOLVING UNKNOWN QUANTITIES
USING THE CONCPT OF EQUILLIBRIUM
FREE BODY
• A free body diagram is a pictorial representation often
used by physicists and engineers to analyze the forces
acting on a body of interest.
• A free body diagram shows all forces of all types acting on
this body. Drawing such a diagram can aid in solving for
the unknown forces or the equations of motion of the
body. Creating a free body diagram can make it easier to
understand the forces, and torques or moments, in
relation to one another and suggest the proper concepts
to apply in order to find the solution to a problem.
• The diagrams are also used as a conceptual device to help
identify the internal forces—for example, shear forces and
bending moments in beams—which are developed within
structures.[
EXAMPLE
EXAMPLE
• A simple free body diagram, shown above, of a block on a
ramp illustrates this.
• All external supports and structures have been replaced by
the forces they generate. These include:
• mg: the product of the mass of the block and the constant of
gravitation acceleration: its weight.
• N: the normal force of the ramp.
• Ff: the friction force of the ramp.
• The force vectors show direction and point of application and
are labeled with their magnitude.
• It contains a coordinate system that can be used when
describing the vectors.
LAWS ON EQUILLIBRIUM
• LAMI’S THEOREM
• CONVERSE OF TRINGLE LAW OF FORCES
• CONVERSE OF POLYGON LAW OF FORCES
PROOF
• LAMI’S THEOREM………
CLASSWORK
BRAIN SCRATCHERS……….
OSMANY HALL
DAY
BEGINS
WITH
NUMERICALS