STATICS
.
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.
Types of equilibrium
With respect to the state of a body, equilibrium may be divided into two categories:
1. Static equilibrium.
2. Dynamic equilibrium.
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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
The first condition of equilibrium stated as follow:
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. Σ F=0
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.
Σ FX=0
and
Σ FY=0
Second condition of equilibrium
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. i.e. Σ =0
STATES OF EQUILIBRIUM
.
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.
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Unstable equilibrium
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
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.
Explanation
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.
Reason of neutral
equilibrium
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."
Positive torque:
If a body rotates about its axis in anti clockwise direction, then the torque is
taken positive.
Negative torque:
If the body rotates in the clockwise direction, then the torque is taken as
negative .
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Center of
gravity
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.
Couple: Two equal, opposite forces acting at two different points of the same body are said to
form a couple.
Torque produced in body due to couple is equal to the product of one of the forces of the couple
and couple arm.
Torque due to couple: In diagram forces F1 and F2 are acting on rigid body the perpendicular
distance of these forces from axis o is OA and OB respectively
Than total torque at point o can be written as
Torque= F1 X OA + F2 X OB
Since F1=F2 =F
So = F x OA+ F x OB
= F( OA+ OB)
= Fxr
Questions
6.1 Answer: No . A body will be equilibrium if no force acts on it or a number of forces acting on the
body and algebraic sum of all these is zero. A single force produces acceleration where as for equilibrium
acceleration must be zero.
6.2 Answer. No, a body will be in equilibrium if clock wise torque is equal to anti clock wise torque.
Single torque produces angular acceleration, so body in equilibrium angular acceleration must be zero.
6.6 answer. This is because the smaller the height of centre of gravity of the body, the car wills more
stable and there will very small chances to overturn.