Conservation of momentum
The law of conservation of momentum state that the total momentum of a closed system does not changes this means that when two objects collide the total momentum of the object before the collision is the same as the total momentum of the objects before the collision is the same as the total momentum of the objects after the collision.
Conservation of momentum is a fundamental law of physics which states that the momentum of a system is constant if there are no external forces acting on the system. It is embodied in newton’s first law.
Let’s we have two interacting particles 1 and 2, possibly of different masses. The forces between them are equal and opposite.
According to Newton’s second law, force is the time rate of change of the momentum, so we conclude that the rate of change of momentum P1 of particle 1 is equal to minus the rate of change of momentum P2 of a particle 2,
$$ \frac{dp1}{dt} = \frac{-dp2}{dt} $$For example If a gun is fired, both the bullet and the gun are very stable at first, means the total momentum before firing is zero.
The bullet gains forward motion on discharge. According to conservation of momentum, the gun gains retrograde motion. A bullet of mass m is fired with a velocity v.
The gun of mass M attains a rectilinear backward velocity u. Before the end, the total speed is zero. Hence the total momentum after firing is also zero.
$$ 0 = mv + Mv $$ $$ u = -\frac{m}{M} v $$where,
u = recoil velocity
m = mass of the bullet
M = mass of the gun
The mass of the bullet is very less than the mass of the gun therefore backward velocity of the gun is very less.
Another example of Conservation of momentum is Rocket propulsion - There is a gas chamber at one end of the rocket.
The gas escapes from this chamber with great velocity.
The total momentum is zero before the gas is expelled. Due to the ejection of gas from the rocket, the rocket acquires recoil velocity and acceleration in the opposite direction.
This is due to conservation of momentum.
The principle is followed in this take off of rocket is the propulsion of all rockets, jet engines, deflected balloons, and even squid and octopus is explained by a single physical principle which is Newton's third law of motion. Matter is forcefully ejected from a system, producing an equal and opposite reaction on what remains.
Example : Use of momentum
Typical of a ball-bat collision, the bat's momentum dominates and the ball flies in the opposite direction from where it came.
If we increase the weight of the bat and swing it with the same speed, we get a considerable increase in bat momentumt that results in higher ball exit velocity.
Momentum = mass x velocity