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# Newton's Third Law of Motion

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 Sub Topics You could visualize forces every where when a man walks, a fish swims, a bird flies, a man sits etc. Isaac newton could explain the law behind these interaction forces and called as newtons third law of motion showing action-reaction force pairs. Fish swimming tells about the newtons third law. Here fins push the water backward that moves fish forward exhibits action-reaction force

## What is Newtons Third Law?

The Newtons third law states that: For every action, equal and opposite reaction will be experienced. It illustrates that the action force on the first body is equal to the reaction force given by the second body explaining the action-reaction force pair.
Lets assume that two objects undergoing interaction. If the first objects exerts a force on second body (action force F12) then an equal force will be exerted by the second body on the first (reaction force F21). Thus
F12 = - F21
or
F12 + F21 = 0
This gives Newtons third law of motion.

## Newtons Third Law Equation

Newtons second law relates the force on the body to the acceleration of the body. You know that Force can be realized when the interaction takes place between the bodies as pairs. Take two bodies A and B interacting with each other. Let FBA is the force exerted by A and B and FAB is the force on A by B. Then Newtons third law say that
FAB = - FBA
This tells that FAB and FBA are force equal in magnitude and opposite in magnitude.

## Newtons Third law Experiments

There are couples of experiments demonstrating the newtons third law. Here is the one:

Take two spring balances A and B showing a finely marked readings. Attach one end of spring with the other as shown in figure. If you pull the balance B and observe the readings both the balances shows the same reading tells that equal and opposite force acts. Here the pull is called as action force of the balance B and the other balance is the reaction indicates that FAB = - FBA.

Thus the pull force of one spring on the another gives out the equal force of pull by the other on the one.

## Newtons Third Law Examples

Here are few examples on newtons third law
1. You could be amazed to know what makes the bird to fly? The bird pushes the air down that makes it to fly.
2. While sitting on the chair the body exerts force on the chair and the chair exerts the equal force back expressing the action-reaction force.
3. While getting in to the pool a man jumps from a diving board. He gives a push to the board is a action force and the board in turn gives the man a push forward is a reaction force.

## Newtons Third Law Problems

Here are some problems based on newtons third law you can go through it:

### Solved Examples

Question 1: An automobile of mass 1200 kg moving at 30 ms-1 is brought to rest over a distance of 50 m. Calculate the retarding force and time in which vehicle is brought to rest.
Solution:

Mass m = 1200 kg, Initial velocity u = 30 ms-1, Final velocity v = 0, distance s = 50 m
If a is the acceleration then v2 = u2 + 2as
Acceleration a = $\frac{v^2 - u^2}{2s}$
= $\frac{0 - 30^2}{2 \times 50}$
= $\frac{-900}{100}$
= -9 ms-2
Uniform retardation a = -9ms-2
Retarding force due to force applied is F = ma = 1200 $\times$ 9 ms-2 = 10800 N
If t is the time when vehicle is brought to rest then v = u + at
or
Time taken t = $\frac{v - u}{a}$ = $\frac{0 - 30}{-9}$ = 3.33 s

Question 2: A force of 100 N acts on the body for 5 s imparts a velocity of 20 ms-1. Calculate the mass and momentum of the body.
Solution:

Given: Force F = 100 N, time t = 5s, initial velocity u = 0, final velocity v = 20 ms-1
Let a be the acceleration and we know that final velocity v = u + at
or
Acceleration a = $\frac{v - u}{t}$ = $\frac{20 - 0}{5}$ = 4 ms-2
Mass of the body = m = $\frac{F}{a}$ = $\frac{100 N}{4\ ms^{-2}}$ = 25 kg
At the end of 5s, v = 20 ms-1
Momentum p = mv = 25 $\times$ 20 = 500 kg ms-1.