X Physics - Chapter 6 - Statics

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

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.

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.


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

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.