Conservation of Momentum
If the external force on a system is zero, the momentum of the system remains constant i.e., in an isolated system, the total momentum remains conserved. On the other hand, when two or more bodies act upon one another, their total momentum remains constant provided no external forces are acting on them.
Suppose two balls (Blue & Black), they have masses m_{1} & m_{2} and initial velocities u_{1} and u_{2} as shown in above figure before collision. The two bodies collide and internal force is exerted by each body. After collision balls start moving with velocities v_{1 }and v_{2 }respectively. Note that there is change in their velocities due to collision.
Initial momentum of object 1 = m_{1}u_{1}
Initial momentum of object 2 = m_{2}u_{2}
Final momentum of object 1 = m_{1}v_{1}
Final momentum of object 2 = m_{2}v_{2}
Rate of change of momentum in A, F_{1} = (m_{1}v_{1} - m_{1}u_{1})/ t
Rate of change of momentum in A, F_{2} = (m_{2}v_{2} - m_{2}u_{2})/ t
From 3rd law of motion, F_{1} = - F_{2}
_{or, (m1v1 - m1u1)/ t = - (m2v2 - m2u2)/ t}
or, (m_{1}v_{1} - m_{1}u_{1}) = - (m_{2}v_{2} - m_{2}u_{2})
or, (m_{1}u_{1 + }m_{2}u_{2}) = (m_{1}v_{1} + m_{2}v_{2})
Since, (m_{1}u_{1} + m_{2}u_{2}) is the total momentum of the two balls 1 and 2 before collision and (m_{1}v_{1} + m_{2}v_{2}) is their total momentum after the collision.
The sum of momenta of the two objects before collision is equal to the sum of momentum after the collision, provided there is no external unbalanced force acting on them. This is known as the law of conservation of momentum.
Applications of Conservation of Momentum:
When bullet is fired from a gun, gun recoils in the opposite direction of bullet. The momentum of bullet is equal to momentum of gun. Thus, in the case of firing of bullet law of conservation of momentum is applied as usual.
In the collision of atoms, the conservation of momentum is applied.
In the game of snooker, when a ball is hit by stick, the conservation of momentum is applied.
When the mouth of an inflated balloon is let open, it starts flying, because of conservation of momentum.
When a cricket ball is hit by bat, the law of conservation of momentum is applied.
When the coins of carom board are hit by striker, the law of conservation of momentum is applied.
Newton’s cradle is one of the best examples of conservation of momentum.
Newtons Cradle, Source: Wikipedia