## Chapter 4

LIKE PARALLEL FORCES

Like parallel forces are the forces that are parallel to each other and have the same direction.

**UNLIKE PARALLEL FORCES**

UnLike parallel forces are the forces that are parallel but have directions opposite to each other.

ADDITION OF A VECTOR

“The process of combining of two or more vector to produce a signal vector having the combining effect of all the vector is called the resultant of the vector and this process is known as the addition of a vector”.

HEAD AND TAIL RULE

Suppose we have two vector A and B having the different magnitude and direction.

1, First of all chose a suitable scale and representation of all the vector have been drawn on the paper.

2, Put all the vector for finding the resultant of given vector such that the head of the first vector join the tail of the second vector.

3, Now join the tail of the first vector with tail of the second vector such that it join the two vector with head to head and tail to tail by another.

4, The new vector R will be the resultant of the given vector.

5, It can be measured by the Dee or any suitable mean. This method is called the head and tail or tip to tail rule.

## RESOLUTION OF FORCES

“The process of splitting up of a single force into its components is called the resolution of a forces”

Fx= F Cosα

Fy= F sinα

## USING PERPENDICULAR COMPONENTS

F=√ (F2X+F2Y)

Ѳ=Tan-1 =Fy/Fx

Moment Arm (L)

The perpendicular distance between the axis of rotation and the line of the action of force is called the moment arm of the force.

## Principle of Moments

The body is balanced if the sum of the clockwise moments about a point is equal to sum of the anticlockwise moments about that point.

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

= F * L

## CENTRE OF MASS

Centre of mass of a system is such a point where an applied force causes the system to move without rotation.

CENTRE OF GRAVITY

The centre of gravity is a point at which the whole weight of the body appears to act vertically downward.

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 diagonals.

4. Parallelogram: Point of intersection of the diagonals.

5. Sphere: Centre of the sphere.

COUPLE

A pair of forces of equal magnitude acting in parallel but opposite directions

EQUILIBRIUM

“A body is said to be in equilibrium condition if there is no unbalance or net force acting on it.”

A body will be in equilibrium if the forces acting on it must be cancel the effect of each other.

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 equal to zero, then the body is said to be in first condition of equilibrium.”

ΣF=0

ΣFx=0 ΣFy=0 ( In terms of X and Y-components)

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.”

= 0

STATES OF EQUILIBRIUM

There are following three states of Equilibrium:

1.Stable Equilibrium

A body is said to be in stable equilibrium if after a slight tilt it returns to its previous position.

OR 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. Unstable Equilibrium

A body is said to be in unstable equilibrium if after a slight tilt it does not returns to its previous position. OR

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. **Neutral equilibrium**

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.