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SCIENCE-9

Chapter 2 - Force and Motion

INTRODUCTION

while travelling on the bus, what do we feel when it stops or moves suddenly? Why does it happen? Such types of incidents felt by us in our daily life. In this lesson, we will study about those facts, principles and rules related to them.

Definition:
Force is defined as the push or pull which change or tends to change the position of the body from rest to motion or from motion to rest.
Or, Force is an agent or influence that causes a free body to change its state direction and shape / size. Its unit is Newton. The force that is applied to a body of mass one kg to produce an acceleration of one m/s2 is known as one newton.
1N = 1kg × 1m/s2= 1 kgm/s2

Balanced Force: When force acting on a body from different direction do not change the states of rest or motion of an object, then it is said to have balanced force. Its net resultant is 0.

Unbalanced Force: When force acting on a body from different direction changes the state of rest or of motion , such forces are unbalanced force. Its resultant is non-zero


REST AND MOTION

Key points:

  • They are relative terms. (The same object may be at rest with respect to an object but in the motion with respect to another object. for example: in moving bus, passengers are at rest with respect to each other, but the bus and the passengers are in motion with respect to the nearby trees, poles, etc.)
  • None of the objects are absolutely at rest or in motion.
  • Whether an object is at rest or in motion, it depends on observer.
  1. Rest:
    An object is said to be in rest for an observer if the position of the object does not change with respect to the observer. We wait for our school bus or sleep at night are some example of rest. To be an object in rest, it must not occupy any space.

  2. Motion:
    An object is said to be in motion for an observer if the position of the body changes with respect to the observer. To be an object in motion, it must occupy some space. Flying aero plane, running car are some example of bodies in motion.
    What is the relation between rest and motion?
Speed and Velocity

The total distance covered by an object per unit time in any direction is called its speed. Its SI unit is meter per second (m/s). Speed is a scalar quantity as it has only magnitude but no direction.
Formula: Speed=(total distance covered in any direction) / (time taken)

The total displacement covered by an object per unit time is called its velocity. Its SI unit is meter per second (m/s).Velocity is a vector quantity as it has both magnitude and direction.
Formula: Velocity=   (total displacement) / (time taken)
Distance is scalar quantity but displacement is vector, why?

Uniform-Velocity: If an object covers equal distance in equal interval of time is called uniform velocity.
To become the uniform velocity, the direction of the speed must have a fixed direction. It is not said a uniform velocity if an object is moving in a circle

Non-Uniform-Velocity: If an object covers unequal distance in equal interval of time in a straight line in a fixed directions called uniform velocity. Or, if it covers an equal distance in each second in different directions, it is also said to be in non-uniform velocity.

Acceleration

The rate of change of velocity is called acceleration
Its unit in SI is m/s2.
Lets elaborate it with one example If you apply more force on the peddle of your bicycle, the velocity of the bicycle increases and if you apply the brake, its velocity decreases. Here, the motion of the bicycle is called accelerated motion.
Acceleration = (change in velocity) / Time taken
.
or, Unit of acceleration = (unit of velocity ) / (unit of time)
or, unit of acceleration = (m/s) / s
or, unit of acceleration=m/s2
Net acceleration = (final velocity - initial velocity) / Time taken

- If the acceleration of an object is constant throughout the motion is called uniform acceleration.

- If the acceleration of an object is not constant throughout the motion is called non uniform acceleration.


Equations of Motion

let,
S = displacement
U = initial velocity
V = final velocity
A = acceleration
T = time
Now,
  1. First Equation of Motion :
    v = u+at
    we know that,
    a = (v - u) / t
    v - u = at
    v = u + at
  2. 2nd Equation Of Motion
    s = {(u + v) / 2} × t
    we know that,
    a - v = (u + v) / 2
    s/t = (u + v) / 2
    s = {(u + v) / 2} × t.
  3. 3rd Equation Of Motion
    v2 = u2 + 2as
    we know that,
    v = u + at
    t = (v - u) / a
    and, s = {(u + v) / 2} × t
    Substituting the value, we get
    s = {(u + v) / 2} × {(v - u) / a}
    s = (v2 - u2) / 2a
    v2 - u2 = 2as
    v2 = u2 + 2as
  4. u Fourth Equation of Motion :
    s = ut + 1/2(at2)
    Derive yourself, if any problem ask in question section.
Inertia

The tendency of a body to continue its state of rest or uniform motion in a straight line is called inertia. It is of two types:

  1. INERTIA OF MOTION:

    Anything that continue its state in motion or, the inertia presents in moving bodies is known as inertia of motion.
    For example:Due to the inertia of motion, a fan keeps on moving for some time even after the electricity is switched off. Electric fan runs because of electric power, but it keeps on moving even after the electric supply is cut off. The fan should be stopped as soon as the switch is off but it doesn’t stop because of inertia of motion.

  2. INERTIA OF REST:

    Anything that continue its state in rest or, the inertia presents in resting bodies is known as inertia of rest.
    For example: Due to inertia of rest, a mango fruit falls down from the branch while shaking it forcefully. In the beginning, the fruit along with the branch remains at rest. When we shake the branch, it comes into motion, but due to inertia of rest, the mango fruit tries to be at rest. As a result of inertia of rest of the fruit, it detaches from the branch and falls down.


Newton's Law of Motion

The famous scientist, Newton, formulate the laws of motion by him and it is now known as newton's laws of motion. He formulates three laws of motion:

Newton's First Law of Motion:

According to Newton's First law of motion, "everybody continues to be in its state of rest or uniform motion in a straight line unless an external force is applied on it". This law is fully depends on law of inertia. It means that, force is required to change the inertia of rest of a body into inertia of motion and inertia of motion of a body into inertia of rest. Hence, Newton’s first law of motion is also called law of inertia.

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”

Mathematically,
-Acceleration(a) α Force(F){when mass of the body is kept constant}
-Acceleration(a) α 1/m {if force is kept constant}
Hence, if force (F) produces an acceleration (a) in a body having mass (m), then from the newton’s second law of motion,
-Acceleration(a) α F / m
-F α ma
-F = kma(here k is a constant)
In equation (iii) if a = 1 m/s2, m = 1 kg, the value of F becomes 1N. So, in this condition the value of k also becomes 1. Therefore;
F = ma

Newton's Third Law of Motion:

Newton’s third law of motion states that “every action has equal but opposite reaction”.

Examples:
-While launching a rocket into the space, the hot gases produced by the rapid burning of fuel rush downward but the rocket goes upward.
-While firing a gun, bullet moves in the forward direction but the gun recoils in the backward direction.



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