Chapter-06
Definitions
1. Static
Statics deals with the bodies at rest
under number of forces, the equilibrium and the conditions of equilibrium.
2. Resultant
Force
The net effect of two or more forces
is a single force, that is called the resultant force.
3. Moment Arm
The perpendicular distance between
the axis of rotation and the line of the action of force is called the moment
arm of the force.
TORQUE
It is the turning effects of a force
about an axis of rotation is called moment of force or torque.
FACTORS ON WHICH TORQUE DEPENDS
1. The magnitude of the applied
force.
2. The perpendicular distance between
axis of rotation and point of application of force.
REPRESENTATION
Torque may be represented as,
Torque = Force * moment arm
T = F * d
Torque may be represented as,
Torque = Force * moment arm
T = F * d
CENTRE OF GRAVITY
The centre of gravity is a point at
which the whole weight of the body appears to act.
Centre of
Gravity of Regular Shaped Objects
We can find the centre of gravity of
any regular shaped body having the following shapes:
1. Triangle: The point of intersection
of all the medians.
2. Circle: Centre of gravity of
circle is also the centre of gravity.
3. Square: Point of intersection of
the diagnonals.
4. Parallelogram: Point of
intersection of the diagonals.
5. Sphere: Centre of the sphere.
Centre of
Gravity of Irregular Shaped Objects
We can find the center of gravity of
any irregular shaped object by using following method. Drill a few small holes
near the edge of the irregular plate. Using the hole A, suspend the plate from
a nail fixed horizontally in a wall. The plate will come to rest after a few
moments. It will be in a position so that its centre of gravity is vertically
below the point of suspension.
Now, suspend a plumb line from the supporting nail. Draw a line AA’ in the plate along the plumb line. The centre of gravity is located somewhere on this line.
Now, suspend a plumb line from the supporting nail. Draw a line AA’ in the plate along the plumb line. The centre of gravity is located somewhere on this line.
Repeat the same process using the
second hole B. This gives the line BB’ on the plate. Also repeat this process
and use hole C and get line CC’.
The lines AA’, BB’ and CC’ intersect each other at a point. It is our required point, i.e.e the centre of gravity. We can use this procedure with any irregular shaped body and find out its centre of gravity.
The lines AA’, BB’ and CC’ intersect each other at a point. It is our required point, i.e.e the centre of gravity. We can use this procedure with any irregular shaped body and find out its centre of gravity.
EQUILIBRIUM
A body will be in equilibrium if the
forces acting on it must be cancel the effect of each other.
In the other word we can also write
that:
A body is said to be in equilibrium
condition if there is no unbalance or net force acting on it.
Static
Equilibrium
When a body is at rest and all forces
applied on the body cancel each other then it is said to be in static
equilibrium.
Dynamic
Equilibrium
When a body is moving with uniform
velocity and forces applied on the body
cancel each other then it is said to be in the dynamic
equilibrium.
CONDITIONS OF EQUILIBRIUM
FIRST
CONDITION OF EQUILIBRIUM
“A body will be in first condition of
equilibrium if sum of all forces along X-axis and sum of all forces along
Y-axis are are equal to zero, then the body is said to be in first condition of
equilibrium.”
( Fx = 0 Fy = 0 )
SECOND
CONDITIONS OF EQUILIBRIUM
“A body will be in second condition
of equilibrium if sum of clockwise(Moment) torque must be equal to the sum of
anticlockwise torque(Moment), then the body is said to be in second condition
of equilibrium.”
Sum of torque = 0
Sum of torque = 0
STATES OF EQUILIBRIUM
There are following three states of
Equilibrium:
1. First
State (Stable Equilibrium)
A body at rest is in stable
equilibrium if on being displaced, it has the tendency to come back to its
initial position.
When the centre of gravity of a body
i.e. below the point of suspension or support, then body is said to be in
stable equilibrium.
2. Second
State (Unstable Equilibrium)
If a body on displacement topples
over and occupies a new position then it is said to be in the state of unstable
equilibrium.
When the centre of gravity lies above
the point of suspension or support, the body is said to be in the state of
unstable equilibrium.
3. Third
State
If a body is placed in such state
that if it is displaced then neither it topples over nor does it come back to
its original position, then such state is called neutral equilibrium.
When the centre of gravity of a body
lies at the point of suspension, then the body is said to be in neutral
equilibrium.
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