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.
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.
1. Static equilibrium.
2. Dynamic 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
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.
For example: Jump by using parachute.
Conditions of equilibrium
There are two conditions of
equilibrium are as follows
First condition of equilibrium
To maintain the transitional
equilibrium in a body the vector sum of all the forces acting on the body is
equal to zero
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 alongY-axis is
zero.
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
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
States of equilibrium
There
are three states of equilibrium:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaEDUIAqq5GQhYytFbhvMptWRcrbHxWspFZ7NQIqlKoiYB1VtCBu3S8UQHTbBN6He2zPCl1DOeUWPEofdZGnPQWwpxhfjjwoT5mxTIToibmhSGZNheocXRAMgg8PIZI25hVTy5h_XTjEs/s1600/4.png)
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
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."
The turning effect of a force
depends upon two factors:
The torque about any axis is
given by the product of force and moment arm
Torque = force x moment arm
Positive
torque:
If a body rotates about its axis in anti clockwise direction, then the torque is taken positive .
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
If the body rotates in the clockwise direction, then the torque is taken as negative
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.
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:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaEDUIAqq5GQhYytFbhvMptWRcrbHxWspFZ7NQIqlKoiYB1VtCBu3S8UQHTbBN6He2zPCl1DOeUWPEofdZGnPQWwpxhfjjwoT5mxTIToibmhSGZNheocXRAMgg8PIZI25hVTy5h_XTjEs/s1600/4.png)
Center of gravity of a rectangular is at the point of intersection of its diagonals
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaEDUIAqq5GQhYytFbhvMptWRcrbHxWspFZ7NQIqlKoiYB1VtCBu3S8UQHTbBN6He2zPCl1DOeUWPEofdZGnPQWwpxhfjjwoT5mxTIToibmhSGZNheocXRAMgg8PIZI25hVTy5h_XTjEs/s1600/4.png)
Center of gravity of a circle is at its center.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaEDUIAqq5GQhYytFbhvMptWRcrbHxWspFZ7NQIqlKoiYB1VtCBu3S8UQHTbBN6He2zPCl1DOeUWPEofdZGnPQWwpxhfjjwoT5mxTIToibmhSGZNheocXRAMgg8PIZI25hVTy5h_XTjEs/s1600/4.png)
Center of gravity of square is at the point of intersection of its diagonals.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaEDUIAqq5GQhYytFbhvMptWRcrbHxWspFZ7NQIqlKoiYB1VtCBu3S8UQHTbBN6He2zPCl1DOeUWPEofdZGnPQWwpxhfjjwoT5mxTIToibmhSGZNheocXRAMgg8PIZI25hVTy5h_XTjEs/s1600/4.png)
The center of gravity of a regular bar is at its geometrical center.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaEDUIAqq5GQhYytFbhvMptWRcrbHxWspFZ7NQIqlKoiYB1VtCBu3S8UQHTbBN6He2zPCl1DOeUWPEofdZGnPQWwpxhfjjwoT5mxTIToibmhSGZNheocXRAMgg8PIZI25hVTy5h_XTjEs/s1600/4.png)
The center of gravity of a triangle is at the point of intersection of its medians.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaEDUIAqq5GQhYytFbhvMptWRcrbHxWspFZ7NQIqlKoiYB1VtCBu3S8UQHTbBN6He2zPCl1DOeUWPEofdZGnPQWwpxhfjjwoT5mxTIToibmhSGZNheocXRAMgg8PIZI25hVTy5h_XTjEs/s1600/4.png)
The center of gravity of a cylinder is at the axis of cylinder.