Unit-2 | FORCE | Class-09

Overview: Force is an external agency that changes or tries to change the position of a body. Here we will discuss about rest and motion, effects of force, vectors and scalars, equations of motions, speed and velocity, acceleration and retardation, and Newton's Laws of Motion.

Force:

Force is an external agency that changes or ties to change the position of an object. In general words, Force is the push or pull acting on an object. 
The SI unit of Force is Newton (kgm/s²) and C.G.S. unit of Force is Dyne (gcm/s²).

Relation between Newton and Dyne:

We know, 
1 Newton = 1 kg × 1 m/s²    [ F = ma ]
= 1× 1000g × 1 ×100cm/s²
= 1000g × 100cm/s²
= 100000 g cm/s²
= 10^5dynes

So, 1 Newton = 10^5dynes

One Newton force can be defined as
the force which prodces 1m/s^2 acceleration on a mass of 1 kg. 

Rest and Motion:

To determine whether a body is in the state of rest or motion, we need to take a reference point. If a body changes its position over time with respect to the reference point, then the body is said to be in motion.If a body doesn't change its position over time with respect to the reference point, then the body is said to be in rest.Example: Suppose we are travelling in a bus. If we take the passengers inside the bus as the reference point, then we have not changed our position over time, so we are in a state of rest. But, in the same condition, if we take the outer surrounding as the reference point, then we are constantly changing our position over time, so we are in a state of motion. Therefore, rest and motion are two relative terms.

Effects of Force:

  • It can change the state (rest or motion) of a body : Suppose that a football is moving in the ground. Then the football is constantly sliding over the ground's surface. Due to this reason, frictional force is produced which causes the football to stop.

  • It can change the direction of a moving body : In cricket, when the bowlers bowl a ball, they throw it in one direction but when the batsman hit that ball with a massive force, that force causes the moving ball to change its direction.
  • It can change the shape of a body : If you apply pressure (force) to a rubber ball, then it changes its shape. 
  • It can change the speed of a moving body : When you apply brake on the car which is moving with great speed, the force you applied while you applied the brake, it causes the car to stop.

Vectors and Scalars:

Vectors are those physical quantities that have both magnitude and a fixed direction. The sum of vectors may be negative, zero or positive. Example: velocity, displacement, etc.

Scalars are those physical quantities that magnitude but no fixed direction. The sum of scalars is always positive. Example: speed, distance, etc.

Distance and Displacement:

Distance is the length between two points. It is a scalar quantity. It is always positive.

Displacement is the length between two points in a certain direction. It is a vector quantity. It may be positive, negative, or zero.


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Speed and Velocity:

Speed is the rate of change of distance. Simply, the distance traveled by a body per unit time is called speed.  It is scalar quantity. It is always positive. Mathematically, Speed = Distance (s) / Time taken (t)

Velocity is the rate of change of displacement. Simply, the distance traveled by a body in a fixed direction per unit time is called velocity. It is vector quantity. It may be positive, negative or zero.Mathematically, Velocity = Displacement (s) / Time taken (t)

Acceleration:

Acceleration is the rate of change in velocity of a moving body.  Acceleration is denoted by 'a'. Its SI unit is m/s^2 . Mathematically, acceleration (a) = final velocity (v) - initial velocity (u) / time taken (t)

i.e. a = (v-u) / tThe negative change is the rate of velocity of a moving body is called retardation.


Graphical Representation of Motion:

The motion of a moving body can be represented in graph through the following ways with two different relations:

1. Distance-Time Graph:

Distance-Time Graph is the graphical representation of the relationship between the distance traveled by a body and the time taken. See the following diagrams to get a better understanding of this graph:



2. Velocity-Time Graph:

Velocity-Time Graph is the graphical representation of the relationship between the velocity of a body and the time taken. Observer the following diagrams to get a better understanding of the various relations in this graph:


Equations of Motion: 

There are three different equations of motion: 

i. v= u+at
Let us consider a body having initial velocity 'u' is moving with the acceleration 'a' and after certain time 't' reaches the final velocity 'v'. Then,
Acceleration (a) = Final velocity (v) - Initial velocity (u)  / Time Taken
a = (v-u)/t 
or, at = v-u
or, v = at + u
or, v = u + at

ii. v^2 = u^2 + 2as
Let us consider a body having initial velocity 'u' is moving with the acceleration 'a' and after certain time 't' reaches the final velocity 'v'. Then,
Average velocity = (v + u) /2
We know, Distance traveled (s)= Average velocity (v av) x Time taken (t) 
or, s = v av x t
or, s = (v + u) /2  x t
or, s = (v + u)/ 2 x (v-u) / a   [ i.e. t = (v-u) / a]
or, s = v^2 - u^2 / 2a
or, 2as = v^2 - u^2
so, v^2 = u^2 + 2as #proved

 iii. s= ut + 1/2 at^2
Let us consider a body having initial velocity 'u' is moving with the acceleration 'a' and after certain time 't' reaches the final velocity 'v'. Then,
Average velocity = Finaal velocity + Initial velocity / 2 
or, v av = (v + u) /2
 We know, Distance traveled (s)= Average velocity (v av) x Time taken (t) 
or, s = ( v + u ) / 2 x t
or, s = (u + at + u) / 2 x t  [ i.e. v = u + at]
or, s = (2u + at) /2 x t
or, s = 2ut/2 + at^2 /2
or, s = ut + at^2 /2
or, s = ut + 1/2 at^2


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Mass and Inertia:

The amount of matter contained in a body is called its mass. Inertia is the inability of a body having mass to change its state of motion or rest by itself. Inertia of a body is directly proportional to the mass of the body. 

Types of Inertia:

Inertia of Rest: 

Inertia of Rest is the inability of a body at rest to change its state of rest by itself. 

Inertia of Motion:

Inertia of Motion is the inability of a moving body to change its state of motion by itself.

Momentum:

Momentum is the product of mass and velocity. Mathematically, Momentum (p) = Mass (m) x Velocity (v)

Newton's Laws of Motion:

1. Newton's First Law of Motion:

Newton's First Law of Motion states that,
Every body continues to be in a state of rest or of uniform motion in a straight line unless an external force is applied on it. 
This law is also called law of inertia.

2. Newton's Second Law of Motion:

Newton's Second Law of Motion states that,
Acceleration produced on a body is directly proportional to the force applied on it and inversely proportional to its mass. 
From Newton's Second Law of Motion:
a ∝ F ..... (1)
and,
a ∝ 1/m .... (2)
Combining (i) and (ii), we get,
a ∝ F/m
or, F∝ m/a ..... (3)
or, F = kma [here 'k' is a constant of proportionality]
Let, F= 1N, m =1 kg and a= 1m/s^2 then
,
k = 1
Now, put the value of k in equation (3),
F= 1.ma
So, F = ma   #proved



3. Newton's Third Law of Motion:

Newton's Third Law of Motion states that, 
To every action there is an equal but opposite reaction.

Balanced and Unbalanced Force:

Forces are said to be balanced force if they do not change the state of rest or uniform motion of a body in a straight line.
Forces are said to be unbalanced force if they change the state of rest or uniform motion of a body in a straight line. 






#Science #Force #Class9 #Numerical #Notes