Law of Conservation of Momentum NCERT Physics Class 12
In physics, there are so many laws that it becomes difficult to memorize all of them, you all have been familiar from different types of laws like law of motion, law of inertia and the list goes on, we can even interpret many laws from its name only like law of motion is related motion ,law of attraction is related to attraction ,so now you can guess From what the Law of Conservation of Momentum is related to? But it is not enough to know only that it is related to which thing. So let’s head towards the real phenomenon of Law of Conservation of Momentum.
Expounding of Law of Conservation of Momentum
Law of Conservation of Momentum can be defined as:
“When two object is colliding is an isolated system, then the total momentum of two objects before the collision is equal to the total momentum of the two objects after the collision.”
We can simply say that if two objects are colliding in an isolated system, the total momentum before and after the collision is equal.
Here we are mentioning isolated system again and again because isolated is that system that does not interact with surrounding, that is its total mass and energy remains same, so there will be no external mass, force or energy which will change the result for momentum.
So let’s try to understand first that What is Momentum? In Newton mechanics, Momentum is the product of the mass and velocity of an object, it is a vector quantity that is it possess both magnitude and direction.
The total momentum before and after the collision is equal because the momentum lost by one object is equal to the momentum gain by the other.
Conservation of momentum
PROVE OF LAW OF CONSERVATION OF MOMENTUM
From the above definition, we conclude that the total momentum of a system is always conserved, therefore during the momentum is transferred from one body to another. So let’s prove this with the help of the equation.
Consider that a collision takes place between two bodies in an isolated system, a force acting on the two bodies are F1 and F2 and the collision time of the bodies be t1 and t2.
Read other notes on Electromagnetic waves from Class 12 Physics
So, from Newton’s third law, we know that
However, the collision time of both the bodies are same, i.e.,
Now, the impulse of body_1 and body_2
Impulse of body_1 = F1×t1
Impulse of body_2 = F2×t2
F1×t1 = F1×t2 = -F2×t2 (As t1=t2)
We know that impulse= force × time, therefore
Impulse 1 = -impulse 2
From Newton’s second law
Impulse= change in momentum
Thus, m1×v1 = m2×v2
Here m1, v1 and me, v2 are the mass and velocity of body_1 and body_2 respectively.
Thus, this implies that,
Momentum gained by one body = Momentum lost by another body
Or you can also prove the equation in the following way given below.
INTER-RELATION B/W CONSERVATION OF MOMENTUM AND NEWTON’S LAW OF MOTION
Conservation of momentum is derived from Newton’s law of motion, that is, both the laws are interrelated with each other. You all have been thinking how and why they are related, Let’s take a look in this matter.
Derivation from Newton’s second law
From Newton’s second law, the force is equal to the product of mass and acceleration of the object, so the product of the mass and acceleration of one object is equal to the product of the mass and acceleration of the other object.
Derivation from Newton’s third law
From Newton’s third law, every action has an equal and opposite reaction, so the force exerted by one object on the other object is equal but opposite to the force exerted by the second object on the first object.
NECESSARY CONDITIONS FOR CONSERVATION OF MOMENTUM
There are some conditions which are necessary for the conservation of momentum, the conditions are as follows:
- One body should be initially at rest.
- Internal forces should be equal to external forces.
- Energy should also be conserved.
- No external force should act on the system.
So these are some simple conditions which are mandatory.
APPLICATIONS OF CONSERVATION OF MOMENTUM
Application of conservation of momentum is more common at the microscopic level.
Gas molecules absorb energy from the surroundings and come into motion, and have some momentum then they collide with other molecules, thus transferring some momentum to another molecule. Therefore following the law of conservation of momentum.
There are so many other applications, which we encounter in our daily life, most common example given by others is in the snooker or pool game, when one ball strikes another ball, providing momentum to the ball satisfies this law, but acceleration, rolling, deacceleration, fraction are the conditions which fail the succession of this law.
Another example is, before launching of the rocket, the total momentum of the rocket and its fuel is zero. During the launch, the downward momentum of the expanding exhaust gases just equals in magnitude to the upward momentum of the rising rocket, so the total momentum of the system remains the same.
However, we encounter more examples at the microscopic level instead of a common level.
The total momentum of a closed system is constant and when objects interact, their total momentum before and after the collision is the same. The law of conservation of momentum is logically equivalent to Newton’s third law of motion. Momentum is conserved for all types of collisions. Law of the momentum of conservation is one of the most powerful laws in physics.
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