Law Of Conservation Of Linear Momentum

“When no outer force is applied to colliding bodies, under such a given system, then the vector summation of individual bodies of the Linear Momentum never changes, and neither is impacted by their one-to-one interaction,” says the Law of Conservation of Linear Momentum.

A statement made by the Law of Conservation of Linear Momentum:

When no external forces exist on a system of two objects after the collision, the summation of their linear momentum stays unchanged. It is unaltered by their mutual interaction, according to the law of conservation of linear momentum.

The law of conservation of linear momentum also asserts that if the net external force on a system is zero, the overall momentum of the system remains constant.

The Formula of Law Of Conservation Of Linear Momentum

Linear momentum is calculated using an item’s mass (m) and velocity (v). It is more difficult to stop an object with more momentum. 

p = mv is the formula for linear momentum. Conservation of momentum refers to the fact that the overall amount of momentum never changes.

If there is no external force acting on the colliding objects, the principle of conservation of momentum asserts that if two objects collide, their total momentum before and after the impact will be the same.

The conservation of linear momentum formula expresses the momentum of a system quantitatively. When the net external force is zero, the system remains steady.

Initial momentum is equal to final momentum:

Pi = Pf

Law Of Conservation Of Linear Momentum Equation

The second law of motion can be used to explain the law of conservation of linear momentum. The variation of linear momentum of a body equals the net external force put on it, according to Newton’s second law of motion.

It can be stated mathematically as:

dP/dt = d(mv)/dt = mdv/dt = ma = Fnet

If a body’s net external force is zero, the rate of change of momentum also is zero, implying that there is no change in momentum.

Principle of Law Of Conservation Of Linear Momentum

Let us take this equation as an example: Fext = 0.

The isolated system is not subjected to any external forces. The rate of change of total momentum does not vary in this case. We can state that regardless of the feature or characteristic of the interaction associated with any system, the overall momentum will remain constant.

Applications of the Law Of Conservation Of Linear Momentum

1. The recoil of a gun:

When a bullet is fired from a gun, the gun gives a large velocity to the bullet in the forward direction. Thus, the bullet acquires momentum In the forward direction. The bullet also exerts a reactionary- force on the gun, which is pushed back and acquires an equal momentum in the backward direction. Since the mass of the gun is much greater than the mass of the bullet, the velocity of receding of the gun is much less than the velocity of proceeding of the bullet. If a bullet is fired by a light gun and other similar bullets by a heavy gun, then the light gun will recede with a larger velocity and is likely to hurt the shoulder of the gunner more severely.

2. Jumping from the boat to the shore:

When a person jumps from a boat to the shore, the boat is pushed away from the shore. Initially, the momentum of the boat plus person is zero. When the person jumps from the boat, he acquires momentum towards the shore. The momentum of the boat plus person remains zero if the boat acquires momentum away from the shore. That is, the boat is pushed away from the shore.

3. Flight of a rocket:

In a rocket, the fuel is burned in the combustion chamber, and the highly compressed hot gases are expelled through a nozzle with a large velocity, thus providing upthrust to the rocket. As more and more of the fuel is burned, the mass of the rocket goes on decreasing, and so the velocity of the rocket goes on increasing.

Conclusion

When characterising the momentum of a system of objects, the Law of Conservation of Momentum comes in handy. In its most basic form, the Law of Conservation of Momentum states that an isolated system’s overall momentum remains constant. An isolated system is one in which the objects in the system are not affected by external factors. Newton’s Cradle is a great visual illustration of momentum conservation. When one ball is moving and comes into contact with the others, the entire system’s momentum is preserved because the momentum of the ball on the other end is transmitted to the ball on the other end.