Transcript Class - Educast

Chapter 6
Equilibrium
STATICS
 Statics is the branch of mechanics which deals with the study
of bodies at rest under a number of forces, the equilibrium,
conditions of equilibrium, types of equilibrium and torque
etc.
Equilibrium
A body is said to be in equilibrium if it is at rest or moving
with uniform velocity.
In other words if the linear and angular acceleration of a
body are zero, the body is said to be in equilibrium.
Or we can say that when two or more forces act on a body
such that their resultant or combining effect on the body is
Zero and the body retains its state of rest or of uniform
motion then the body is said to be in equilibrium.
Example
 A book lying on the table, suspended bodies, all stationary
bodies , jump by using parachute.
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Types of equilibrium
Static equilibrium
 If the combined effect of all the forces acting on a body is zero
and the body is in the state of rest then its equilibrium is termed
as static equilibrium.
For example: All stationary bodies
Dynamic equilibrium
 when a body is in state of uniform motion and the resultant of all
the forces acting upon it is zero then it is said to be in dynamic
equilibrium.
For example: Jump by using parachute.
Conditions of equilibrium
 There are two conditions of equilibrium are as follows
First condition of equilibrium
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To maintain the transitional equilibrium in a body the vector sum of all the forces acting on
the body is equal to zero
i.e.
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In other words we can say that to maintain equilibrium the sum of all the forces acting
along X-axis is zero and the sum of all the forces acting along Y-axis is zero.
i.e.
Second condition of equilibrium
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The second condition of equilibrium stated as follow:
A body will be in rotational equilibrium when the algebraic sum of clock wise torque and
anti clock wise torque is zero.
In other words:
A body will be in rotational equilibrium if vector sum of all the torque acting on the body is
zero.
STATES OF EQUILIBRIUM
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States of equilibrium
There are three states of equilibrium:
Stable equilibrium
Unstable equilibrium
Neutral equilibrium
Stable equilibrium
When the center of gravity of a body lies below point of suspension or support, the body is said to
be in STABLE EQUILIBRIUM. For example a book lying on a table is in stable equilibrium.
Explanation
A book lying on a horizontal surface is an example of stable equilibrium. If the book is lifted from
one edge and then allowed to fall, it will come back to its original position.
Other examples of stable equilibrium are bodies lying on the floor such as chair, table etc.
Reason of stability
When the book is lifted its center of gravity is raised . The line of action of weight passes through
the base of the book. A torque due to weight of the book brings it back to the original position.
Unstable equilibrium
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When the center of gravity of a body lies above the point of suspension
or support, the body is said to be in unstable equilibrium
Example
pencil standing on its point or a stick in vertically standing position.
Explanation:
If thin rod standing vertically is slightly disturbed from its position it
will not come back to its original position. This type of equilibrium is
called unstable equilibrium, other example of unstable equilibrium
are vertically standing cylinder and funnel etc.
Reason of instability
when the rod is slightly disturbed its center of gravity is lowered . The
line of action of its weight lies outside the base of rod. The torque due
to weight of the rod toppled it down.
Neutral equilibrium
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When the center of gravity of a body lies at the point of suspension or support,
the body is said to be in neutral equilibrium. Example: rolling ball.
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If a ball is pushed slightly to roll, it will neither come back to its original nor it
will roll forward rather it will remain at rest. This type of equilibrium is called
NEUTRAL EQUILIBRIUM.
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If the ball is rolled, its center of gravity is neither raised nor lowered. This means
that its center of gravity is at the same height as before.
TORQUE - CENTER OF GRAVITY
 Torque
The torque or moment of force can be define as
 “ The tendency of a force to produce rotation in a body
about an axis is called torque or moment of force."
 The turning effect of a force depends upon two factors:
The magnitude of force (F)
Moment arm (r)
The torque about any axis is given by the product of force and moment arm
 Torque = force x moment arm
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Positive torque:
If a body rotates about its axis in anti clockwise direction, then the torque is taken
positive .
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Negative torque:
If the body rotates in the clockwise direction, then the torque is taken as negative .
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Center of gravity
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The center of a body is that point in the body through which the resultant forces due to the
earth’s attraction posses and through which the whole weight of the body always acts.
OR
Center of gravity of a body is a point where total weight of the body is concentrated.
Every body posses a center of gravity and this is irrespective of the body. Its is not necessary that
the center of gravity should be within the body, but it may also be situated in space out side the
body. Example: center of gravity of a ring is at the center, which is in the space.
Center of gravity of different objects:
Rectangle
Center of gravity of a rectangular is at the point of intersection of its diagonals
Circle
Center of gravity of a circle is at its center.
Square
Center of gravity of square is at the point of intersection of its diagonals.
Regular bar
The center of gravity of a regular bar is at its geometrical center.
Triangle
The center of gravity of a triangle is at the point of intersection of its medians.
Cylinder
The center of gravity of a cylinder is at the axis of cylinder.