Conservation of Momentum - Detailed Explanation of the Principle!

To study this principle, first of all, we should know what the momentum is? Well, momentum is defined as the mass in motion. It can also be defined as the product of the mass and velocity of an object. It is a vector quantity with a magnitude and a direction.

Conservation of momentum, the general law of physics according to which the momentum never changes in an isolated collection of objects.

The law of conservation of momentum states that for any two objects colliding in an isolated system, the total momentum before the collision is equal to the total momentum after the collision.

This is because the momentum lost by one object is equal to the momentum gained by the second object. This is also known as the principle of conservation of momentum.

Conservation of momentum is a consequence of Newton’s third and second law of motion. Suppose that the two objects A and B collide with each other. Then according to Newton’s third law, the force exerted by object B on object A will be equal to the force exerted by an object A on object B. It implies that the two forces act for the same amount of time . i.e.  

FBA = -FAB

According to Newton’s second law, 

Force = Rate of Change of Momentum

It follows that the rate of change of momentum of A is equal and opposite to the rate of change of momentum of B. Since these are vectors, they are of equal length but are in opposite directions.  This means that B loses momentum at the exact rate A gains momentum so that their total momentum remains the same.

According to the law of conservation of linear momentum, if no external force is acting on a system of bodies, then the total momentum of the system remains constant. 

When the net external force is zero, then the rate of change of momentum is zero. Therefore the law of conservation of momentum can be expressed mathematically as

Initial momentum = Final momentum i.e.

Pi = Pf

The rocket fuel burns push the exhaust gases downwards, and due to this, the rocket gets pushed upwards. Motorboats also work on the same principle, it pushes the water backwards and gets pushed forward to conserve momentum.

Question: A shell is fired from a gun with a velocity of 300 m/s making an angle of 60 degrees with the horizontal. It explodes into two fragments when it reaches the highest position. The ratio of the masses of the two pieces is 1 : 3. If the smaller piece stops immediately after the collision. Find the velocity of the other.

Sol:  Velocity at the highest point = 300×cos60

=150 m/s

Using momentum conservation,

150×m=3m/4×v

⇒v=200m/s