Newton`s Laws of Motion

        MOTION

The motion and its causes was one of the main problem for the physicists.It remained unsolved for a long time.Galileo was among-est the earliest scientists who tried to solve this problem and pointed out that the motion of a body continues along a straight line unless there is some force that causes it to change the state of motion.

                           In 1687 Newton in his book "philosophine naturalis principia mathematica" meaning "The mathematical principles of natural philosophy" in which he mainly studied motion,of planets and other heavenly bodies.In his book Newton sums up the basic principles of motion in three laws which are as follows:

           Newton`s First Law Of Motion

                     We observe in every day life that an object at rest remains in the state of rest unless it is acted upon by some external force. For example a book is lying on the table can not change its position by itself  unless a force is applied to change its position.Similarly if we push a ball on the ground it should continue its uniform motion indefinitely but it stops after covering certain distance.As soon as the ball starts moving, a force (force of friction) comes into play which opposes the motion of the ball.

                                  These observations were summed up by newton in his first law of motion which states that

                 "Every object continues its state of rest or of uniform motion in a straight line unless it is acted upon by an external force which changes its state of rest or of uniform motion."

The following two conclusions can be drawn from newton`s first law of motion.

1) Force is an agent which produces or tends to produce change in the state of rest or of motion of an object.

2) All the material objects possess the property of opposing any change in their shape of rest or of uniform motion.This property of matter by virtue of which an object resists a change in its state of rest or motion is called inertia.Thus Newton`s first law of motion is also called the law of inertia.

                                                  

  Newton`s Second Law of motion

                 

                              Newton`s first law of motion has given us a simple definition of  force as an agent that changes or tends to change the state of rest or motion of an object.For the determination of this force ,through mathematical calculation,Newton derived a definite relationship between the force acting on an object,the mass of the object,and the acceleration produced.

Newton summarized these results in the form of a law which is known as Newton`s Second Law of Motion.It is stated as,

"When a force acts on an object,it produces acceleration in the object in its own direction.This acceleration is directly proportional to the magnitude of the applied force."

DERIVATION

Suppose a force F is applied on an object of mass M which produces acceleration A in the direction of the applied force then the relationship between acceleration and force can be mathematically expressed as:

                                                             A∝F

Similarly for acceleration and mass the relationship can be written as:

                                                            A∝ 1/M

 combining equations 

                                                           A∝ F/M

Or                                                      F ∝ MA

                                                          F = K.MA

                        where K is constant of proportionality

    Irrespective of any system of units,if the acceleration produced in body of unit mass is unity when a force of unit magnitude is applied,then obviously K=1,  So

                                                          F = MA

In the system international,the unit mass is kg and that of acceleration is m/s^2, the corresponding unit of force is kg m/s^2 which is termed as Newton(N).

  Thus force acting on a body is said to be of 1 newton if it produces acceleration of 1 m/s^2 in the body of mass 1 kg in the direction of the applied force. 

Newton`s Third Law of Motion

Before describing Newton`s third law of motion let us consider the following examples,

1)Place your hand on a table and press it hard in the downward direction,you will feel that the table is also exerting a force on your hand in the upward direction.The force applied by your hand on the table in the downward direction is called action while the push up of the table on your hand in the upward direction is called reaction.

2) Consider a book of weight W which is placed on a horizontal table.It pushes the table with a force F in the downward direction.This is action of the book on the table.In response to this action the table also pushes the book in the upward direction.Since the book is at rest,the resultant force F acting on  the book must be zero that is 

                                      F=0

Two Forces are acting on the book.They are:

                  1)The force of gravity acting downward also called weight of book.

                  2)The push of table on book in upward direction.

               These two forces are equal and opposite to keep the book in stationary position.

SO Newton`s Third Law of Motion states that:

                                

                     "To every action there is always an equal and opposite reaction."