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Newton's Laws of Motion

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Sir Isaac Newton was an English mathematician. He was born on Christmas day in 1642. He has put forward some important concepts, in his classical work Principia, written in 1686. He propose three laws, these laws are known as Newton's laws of motion. These laws form the basis for modern mechanics. It is these laws that provide the basis for the subbranch of mechanics called kinetics.

Newton's Laws of Motion play an important role in explaining the close relationship between motion and force. Newton's first law of motion gives a precise definition of 'inertia' and 'force'. Newton's second law of motion establishes the relation between force and momentum whereas third law of motion establishes the relationship between the 'action' and the 'reaction' forces. Newton was the first to propose that uniform motion was possible when there is no net force acting on a particle.

Newtons Three Laws of Motion

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First law of motion:

Every body continues to be in its state of rest or of uniform motion unless otherwise disturbed by an external agency, such as an unbalanced force or a moment.
Example for first law of motion:
  1. An object lying anywhere keeps on lying there only unless someone moves it from there. For example a table, a chair, a car etc., cannot change their position on their own. Similarly, a body in uniform motion cannot stop on its own. This gives the example for first law of motion.
  2. If a piece of paper placed under a pile of books is suddenly pulled, it does not disturb the pile of books: Initially both the piece of paper and the pile of books are in the state of rest. When the piece of paper placed under a pile of books is suddenly pulled, it is set into motion, while the pile of the books remains in the state of rest due to the inertia of rest. Thus the pile of the book dose not fall.
Second law of motion:

When a force is acting on a body, the force is equal in magnitude of the rate of change of momentum in the body, and acts in the direction of the change in momentum.

In mathematical form we can write

$Force = Mass \times Acceleration$

$F = m \times a$
Example for Second law of motion:

If two bodies of different masses are moving with the same speed or velocity, the force needed to stop the heavier body is more than that required for the lighter body. Lets take the example of cricket ball and the tennis ball moving with same speed. Cricket ball is heavier than tennis ball, hence cricket ball requires more force to stop its motion.
Third law law of motion:

Every action has an equal and opposite reaction; action and reaction forces act on different bodies.
Example for Third law of motion:
  1. A gun recoil when a shot fired from it: when a gun is fired, the bullet goes out due to the force applied on it through the trigger. And the gun recoil in the opposite direction.
  2. In case of a person moving forward during swimming: when a person swims, he pushes the water in the backward direction with his hands and the water pushes the person in the forward direction with an equal force.

Newton Laws of Motion Examples

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The solved examples of newton laws of motion is given below.

Solved Examples

Question 1: What is the acceleration produced by a force of 12N exerted on an object of mass 3kg.
Solution:
 
Given, 

Force (F) = $12N$
Mass (m) = $3kg$
Acceleration (a) = ?

By second law of motion, 

$F = ma$

$12 N$ = $3kg \times a$

$a$ = $\frac{12N}{3kg}$ = $\frac{12 kgm/s^{2}}{3kg}$

= $4 m/s^{2}$ 

Thus the acceleration produced in the object is $4 m/s^{2}$

 

Question 2: What force would be needed to produce an acceleration of $4 m/s^{2}$ on a ball of mass $6 kg$.
Solution:
 
Given, 

Force (F) = ?
Mass (m) = $6kg$
Acceleration (a) = $4 m/s^{2}$

By second law of motion, 

$F = m \times a$

$F$ = $6 kg \times 4 m/s^{2}$

$F$ = $24 kg m/s^{2}$

$F$ = $24 N$

The required force is $24 N$