In terms of physics conservation means something that doesn’t change. The meaning of that statement is that the variable in an equation that represents a conserved quantity is constant over time or in other words it doesn’t changes with time no matter what. It has the same initial and final value both before and after an event. In physics three fundamental quantities are conserved and these are momentum, angular momentum and energy. Conservation of momentum is generally related to collision but it is only applicable to isolated system.
In conservation of momentum the initial momentum is equal to final momentum. And mathematically, it can be given by –
P1i + P2i +… = P2i + P2f
Where subscript i denote initial momentum and f denotes final momentum.
The logic behind momentum conservation
Let us assume two objects O1and O2 and let the force acting between these objects be F1and F2. These forces are vector quantity and are equal to each other in magnitude and in opposite direction. Mathematically it can be expressed as-
F1 = -F2
These two forces experiences equal magnitude and hence they are opposite in direction.
And let T1 and T2 be the time on individual forces. Since the forces acting between two objects are equal and opposite in magnitude and hence they will experience impulse which can be written in the form of –
F1*T1 = – F2*T2
The impulse is equal in equal in magnitude and opposite in direction.
But the impulse that is experienced by an object is equal to the change in momentum of that object (the impulse-momentum change theorem). Therefore each object experiences equal and opposite impulses and that is the only reason that it follows logically that they must also experience equal and opposite momentum changes. As an equation, this can be stated as-
m1 *v1= – m2*v2
The momentum which is vector in quantity experiences changes that are equal in magnitude and opposite in direction.
Interesting facts about conservation of momentum
- Momentum is a vector quantity and that is the only reason we use vector addition to find resultant momentum. The interesting fact about this is that if we consider two objects and they are moving with equal and opposite direction but with equal speed. The vectors being in opposite magnitude and sign will cancel out. That means, the momentum of the body will be zero even though objects are moving.
- Let us assume there is bouncy ball mass m is thrown and it bounces back with velocity v. The wall is well attached to the earth and doesn’t move, yet the momentum of the ball has changed by 2m. If the momentum is conserved, then the momentum of the earth and wall also must have changed by 2mv. We just don’t notice this because the earth is so much heavier then the bouncy ball.
Example: The recoil of cannon is probably familiar to anyone who has watched pirate movies. This is a classic problem in momentum conservation. Consider wheeled, 500 kg cannon firing a 2 kg cannonball horizontally from a ship. The given ball leaves the cannon at the speed which is traveling at 200 m/s. At what speed do the cannon recoil as a result?
Solution : According to conservation of momentum –