Force and Laws of Motion: Part 2

Momentum: –

The quantity of motion possessed by a moving body is known as momentum of the body.

Momentum of a body may be defined as the product of the mass of the body and the velocity of the body. It is denoted by ‘p’

According to definition of momentum,

Momentum = mass velocity

Or P = mv

S. I. Unit of momentum is kg m /s

CGS Unit of momentum is g cm /s

Momentum is a vector quantity and the direction of momentum of a body is same as that of the direction of the velocity of the body.

Newton’s Second Law of Motion: –

Newton’s second law states that, the rate of change of momentum of a body with respect to time, is directly proportional to the force acting on the body and the change in momentum takes place in the direction of applied force on the body.

i.e. force appliedrate of change of momentum

or

Where dp = change in momentum and dt = time taken for this changes

Let mass of the body be m initial velocity u and final velocity v then the change in momentum will be mv – mu in time t

or

or Where a = acceleration

Where k is the constant of proportionality and in S.I. and CGS system, the value of k = 1

Newton’s second law of motion gives the relationship between the force applied on a body and the acceleration produced in the body.

Force can be measured by using Newton’s Second law of motion.

Since by Newton’s second law of motion

F = ma

This equation shows that

(i) A large acceleration is produced in a body if a large force acts on the body and

(ii) A large acceleration is produced in a body of small mass, while a small acceleration is produced in a body of large mass if same force acts on both the bodies.

The S.I. unit of force is Newton or kg m/s²

Or N = kg m/s²

Or 1 N = 1 kg m/s²

The CGS unit of force is dyne or gm cm/s²

CGS unit of force = CGS unit of mass CGS unit of acceleration

or 1 dyne = 1 gm cm/s²

Definition of Newton: –

When m = 1 kg, a = 1 m/s²

then F = ma

F = 1 kg 1 m /s²

or F = 1 kg m /s² = 1 Newton

Hence the force is said to be 1 Newton, if its produces 1 m/s² acceleration in a body of 1 kg mass.

Definition of Dyne:

When m= 1g

a = 1 cm / s²

then F = ma

F = 1g 1 cm /s²

or F = 1g cm/s² = 1 Dyne

Hence, the force is said to be 1 dyne, if it produces 1 cm/s² acceleration in a body of 1 g mass.

Relation between Newton and dyne

We Know that,

1 N = 1 kgm/s²

Now 1 kg = 1000 g

1 m = 100 cm

1 N = 1000 g 100 cm/s²

Or, 1 N = 10³ 10²g cm/s²

Or 1N = 10⁵ gcm/s²

Or 1 N = 10⁵ Dyne (1 Dyne = 1 gcm/s²)

Newton’s third law of motion

Newton’s third law of motion states that, to each and every action, there is an equal and opposite reaction.

Note: Action and Reaction act on two different bodies

Consider a wooden block lying on the horizontal surface of a table shown in fig. below

The weight of the block acts vertically downward. This weight of the block is known as the action and it acts on the surface of the table. The surface of the table exerts an upward force on the wooden block.

This upward force acting on the wooden block is known as reaction. Thus we find that action and reaction act on two different bodies.

Example: –

When a ball strikes against a floor, it exerts a force (known as action) on the floor. According to Newton’s third law of motion, the floor exerts an equal and opposite force (known as reaction) on the ball. Due to this reaction, the ball rebounds.

According to Newton’s third law of motion, action and reaction are always equal to each other. But they can not cancel out each other because they act on different bodies.