EQUILLIBRIUM

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EQUILLIBRIUM

• BY
• GP CAPT NC CHATTOPADHYAY

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MEANING

• Latin aequilibrium,  equivalent to aequi- equi-
    libr ( a ) balance -ium ium
• -ium a suffix found on nouns borrowed from
  Latin, especially derivatives of verb
• Synonyms  equipoise, steadiness, stability.

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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.

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AFTER A LOT OF STUDIES
EXAMPLE OF EQOUILLIBRIUM
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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 ITS 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

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EXAMPLES
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REAL TIME SITUATIONS

• BODY IS IN MOTION N, t, V ?
• BODY IS IN ROTATION N, t, V ?
• COMBINED ACTION OF MOTION AND ROTATION
• BODY IS AT REST N, t, V ALL ZERO

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CONDITIONS

• MOTION- ?F 0
• ROTATION- ?M 0
• COMBINED ACTION - ?F 0, ?M 0
• REST - ?F 0, ?M 0

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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.

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COMPLEX BODY
COMPLEX STRUCTURES POSE DIFFICULTY IN ANALYSIS
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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

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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 forcesfor example,
  shear forces and bending moments in beamswhich
  are developed within structures.

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EXAMPLE
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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.

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LAWS ON EQUILLIBRIUM

• LAMIS THEOREM
• CONVERSE OF TRINGLE LAW OF FORCES
• CONVERSE OF POLYGON LAW OF FORCES

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PROOF

• LAMIS THEOREM
• CLASSWORK

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BRAIN SCRATCHERS.
OSMANY HALL
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• DAY
• BEGINS
• WITH
• NUMERICALS