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CBSE Physics | Force and Laws of Motion: Part 2

August 31st, 2015

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 clip_image002velocity

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 appliedclip_image004rate of change of momentum

or clip_image006

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

clip_image008 clip_image010

or clip_image012

or clip_image014 clip_image016 Where a = acceleration

clip_image018

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

clip_image020

clip_image022

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

clip_image008[1] clip_image025

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 clip_image002[1]m/s2

Or 1 N = 1 kg m/s2

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

clip_image028 clip_image030

clip_image008[2] CGS unit of force = CGS unit of mass clip_image002[2]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

clip_image034 F = 1 kg clip_image002[3]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

clip_image008[3] F = 1g clip_image002[4]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

clip_image008[4] 1 N = 1000 g clip_image002[5]100 cm/s2

Or, 1 N = 103 clip_image002[6]102g cm/s2

Or 1N = 105 gcm/s2

Or 1 N = 105 Dyne (clip_image008[5]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

image

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.

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CBSE Physics Tutorials | Motion: Speed, Velocity and Acceleration

August 31st, 2015

Motion: Speed, Velocity and Acceleration

Speed:

Speed of a body is defined as the distance travelled by it per unit time.

i.e clip_image002hence S.I Unit of speed is metre /sec. (m /s or ms – 1)

Uniform speed:

If a moving body covers equal distances in equal interval of time, then the speed of the body said to be uniform speed

Example:

Suppose a car travels 5 m in every second throughout its Journey then the speed of this car is uniform.

Non- Uniform Speed:

If a moving body covers unequal distances in equal interval of time, then the speed of the body is said to be non uniform speed.

Example:

Suppose a car travels 5 m in first second, 10 m in second second, 7 m in third second, 9 m in fourth second, and so on. Then the speed of this car is changing with time and is said to be non- uniform.

Average Speed: –

Average speed of a moving body is defined as the ratio of the total distance travelled by it to the total time taken by it to cover the distance.

Thus Vav clip_image004

Example: –

When a bus starts its journey from a bus stand, it moves slowly and then its speed is increased Now if it enters a crowded road its speed decreases.

After crossing the crowded road, its speed increases. After traveling few kilometers, suppose the bus has to be stopped, then its speed again decreases. Thus we see that the bus is not moving with the same speed during the whole journey.

Now if we added total distance covered by the bus with different speeds and divide it by the total time taken, then we get the average speed of the bus.

Velocity: –

Velocity of an object is defined as the displacement of the body per unit time

OR,

Velocity of an object is defined as the distance travelled by it per unit time in a particular direction.

i.e. clip_image006

Hence S.I. unit of velocity is metre /sec (m/s)

Uniform velocity: –

If a moving body covers equal displacement (i.e. equal distance in a particular direction) in equal intervals of time, then the velocity of the body is said to be uniform velocity.

Example: –

Suppose a car travels 5 m in every second in a particular direction then the velocity of car is uniform.

Non- uniform velocity: –

If a moving body makes unequal displacement in equal interval of time, then the velocity of the body is said to be non-uniform velocity.

Example: –

Let a car moves over a horizontal road along the east direction. Let its cover unequal distances in each hour, then the velocity of this car is non uniform.

Average Velocity: –

when the velocity of an object changes with time, then the average velocity is defined as the ratio of the total displacement made by it to the total time taken by it

clip_image008

Note:

If the velocity of an object changes at uniform rate in a particular direction, then the average velocity of the object is equal to the mean of the initial and final velocities of the object.

i.e. clip_image010

where u = initial velocity of the object

v = final velocity of the object

Note: –

Velocity of a body can be changed in two ways.

(i) By changing the speed of the body while keeping the direction of motion of the body same.

(ii) By changing the direction of motion of the body, but keeping the speed of the body same.

e.g. The velocity of a ball dropped from the top of a building changes, because its speed changes although its direction of motion remains the same.

Also, the velocity of a car, moving in a circular path changes, because its direction of motion changes continuously although it is moving with a constant speed.

Difference between speed and velocity

Speed

Velocity

1. Speed of a body is defined as the distance travelled by it per unit time i.e. clip_image012

2. Direction is not associated with speed.

3. Speed is a scalar quantity.

4. Speed is always positive.

5. Its value can not be zero for a moving body.

1. Velocity of a body is defined as the displacement of the body per unit time i.e. clip_image014.

2. Direction is associated with velocity

3. Velocity is a vector quantity

4. Velocity can be positive or negative

5. Its value is zero if initial and final position of the body is same.

Acceleration: –

In non-uniform motion, the velocity of a body changes with time. The change in velocity of an object with time is expressed by a physical quantity known as acceleration.

Acceleration tells us, by how much amount the velocity of a body changes in unit interval of time.

In other words, the acceleration is a quantity which measures how quickly the velocity of a body or an object changes

Acceleration of a body is defined as the change in velocity per unit time

i.e. clip_image016

clip_image018 acceleration clip_image020

Acceleration is a vector quantity and its unit is m/s/s or m/s2 or ms – 2

Uniform Acceleration:

If the velocity of an object changes by an equal amount in equal interval of time, then the acceleration of the object is known as uniform acceleration.

e.g. acceleration of freely falling body

Acceleration of a ball rolling down on a smooth inclined plane.

Non- uniform acceleration:

If the velocity of an object changes by an unequal amount in equal interval of time, then the acceleration of the object is known as non-uniform acceleration.

e.g. acceleration of a bus on a crowed road

Uniform circular motion:-

The circular motion of a body having constant or uniform speed is known as uniform circular motion.

How uniform circular motion is an accelerated motion?

When a body moves in a circular path with constant speed, its direction of motion changes continuously.

It means that the body moving in a circular path, changes its velocity. And we know that the change of velocity of a body with time gives rise to an acceleration.

Thus the uniform circular motion is accelerated motion.

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