# Motion and Force

## Definition of Motion

An object is said to be in motion if it changes its position with respect to its surrounding. For example motion of car, flying birds.

## Displacement

The minimum distance between the initial and final point is called as displacement.

OR

The shortest distance between two points is called as displacement.

S.I Unit for displacement is Meter which is denoted as (m)

## Velocity

The change in its position in a unit time or 1 second is called as velocity. The formula for velocity is

Velocity = distance/time

V= S/t

S.I UNIT for velocity is Meter/second (m/sec)

### Average Velocity

The average of two or more than two velocities is called as average velocity. The formula for  Average velocity is

V= V1+V2+V3/3

### Instantaneous Velocity

The velocity of an object at a particular instant of time is called as instantaneous velocity.

## Acceleration

The change in velocity in a unit time or 1 second is called as acceleration. The formula for acceleration is

Acceleration=velocity/time

A = v/t

S.I  unit for acceleration is Meter/second2 (m/sec2)

### Uniform Acceleration

When the velocity of a body changes at equal interval of time it is called as Uniform Acceleration.

### Average Acceleration

The average of two or more than two accelerations is called as average acceleration. The formula for average acceleration is

A= A1+A2+A3/3

### Instantaneous Acceleration

The acceleration of an object at a particular instant of time is called as instantaneous acceleration.

### Equations of Uniformly Accelerated Rectilinear Motion

There are three equations of linear motion.

Vf =vi+ at

S=vit+1/2 at2

Vf2=vi2 =2aS

These are three equations for motion under gravity.

Vf =vi+ gt

h=vit+1/2 gt2

Vf2=vi2 =2gh

## Newton’s Law of Motion

### First Law of Motion

First law of motion states that, A body remains in rest or continue to move until or unless an external force acted upon it. It is also called as law of inertia. Because a body can maintain its state of rest or uniform motion due to its principle feature inertia.

#### Inertia

The state maintaining property of a body is called as inertia.

### Second Law of Motion

Second law of motion states that, When an unbalanced force is applied on a body some acceleration will produce it will cover some distance which is directly proportional to the applied force and it will produce an acceleration in the direction of motion. First consider that the force is directly proportional to the mass and acceleration.

### Third Law of Motion

Third law of motion states that, Every action having an equal reaction but opposite in direction. For example walking on ground, launching of rocket.

## Motion of Bodies Connected By String

### Case 1

Consider two bodies of unequal masses m1 and m2 connected by a string which passes through a frictionless pulley.

Let m1 is greater than m2. Body

A has greatest mass than body B.

First consider the motion of body A. There are two forces acting on it

1. Weight on the body acting downward w=mg

2.Tension on the string.

We have the equation of motion for the body A.

m1g – T=m1a——- eq1

Now consider the body B. here forces will act on the body B

The tension of string acting upward and the weight acting vertically downward.

So the relation become

T- m2g = m2a—–eq 2

By adding both equations eq1 and eq2

m1a+m2a = m1g – m2g

a = (m1-m2/m1+m2)g

Now tension in the string can be calculated as

M1g – T/T-m2g = m1/m2

Now we will cross multiply

M1m2g – m2T = m1T – m1m2g

Or

T (m1+m2) = 2m1m2g

T= (2m1m2/m1+m2)g

### Case 2

When one body moves vertically and the other moves on a smooth horizontal surface.

Consider two bodies A and B of masses m1 and m2 respectively. This passes through a frictionless pulley. The body A is hanging over a string with acceleration a. and body B moves on the horizontal

surface with the same acceleration.

From the above relation

m1g – T=m1a——- eq1

Now consider the body B. here forces will act on the body B The tension of string acting horizontally toward pulley.  The weight acting vertically downward. The reaction R of the smooth horizontal surface on the body which acts vertically upward.

So the relation become

T = m2a—–eq2

To obtaining the value of a

M1g – T = m1a

T= m2a/m1g= (m1a +m2a)

Or (m1+m2)a = m1g

Therefore

A = (m1/m1+m2)g

Putting this value of a in eq II

T = (m1*m2/m1+m2)g

## Momentum of a Body

The quantity of motion is called as momentum.

OR

The product of mass and velocity is called as momentum.

### Units of Momentum

Momentum = mass * velocity

= kg*meter /sec

We get,

Momentum = kg *meter/second* second/ second

= kilogram * (meter/(seconds)2)* second

= kilogram * (meter/(seconds)2) = 1 newton

Momentum = newton-second

### Isolated System

A thermodynamic system which is completely enclosed by walls through which can pass neither matter nor energy, though they can move around inside it.

### Law of Conservation of Momentum

Law of conservation of mass states that, When there is no external force acting on a system then the total momentum of  the system remains constant.

#### Explanation

Consider the isolated system. Let the system consist of two objects A and B of masses m1 and m2 with velocities U1 and U2 respectively before collision. After collision there velocities become v1 and v2 respectively.

Total momentum before collision is M1u1 +m2u2

Total momentum after collision is M1v1+m2v2

When two bodies collide with each other at time interval. m2v2- m2U2/t  average force acting on body

m1v1 – m1U1/t  as both the forces are opposite the relation become

m2v2-m2u2/t = -m1v1 – m1u1/t

or (m2v2 – m2u2) = – (m1v1 – m1U1)

m2V2-m2U2 = m1v1+m1u1

m1u1+m2u2 = m1v1+m2v2

this is the relation for law of conservation of mass.

## Friction

The opposing force produce during the motion is called as friction.  When a liquid or gas flow this type of friction is called as viscosity.

### Coefficient of Friction

The ratio of limiting friction to the normal reaction acting between two surfaces in contact is called the coefficient of friction and usually denoted by m.

m=F/R