Linear momentum and its conservation

Introduction 

Sometimes interaction between two bodies is so fast that it is difficult to measure the forces acting between them and the time of interaction. So in order to predict the speed and direction of motion after interaction the concept of the linear momentum and its conservation is used.

What do you mean by linear momentum?

We all know that position, acceleration and velocity are physical quantities used to describe motion of an object. Now, I will be introducing another physical quantity that will relate body’s state of motion with the forces acting on the body. We know that, one body has the capability to exert force on another body on its way, this capability is measured by linear momentum.

 What is an impulse?

 If you see someone playing billiards, the amount of linear momentum received by the ball depends on the knock it receives from the cue. You can also notice that the linear momentum of the ball varies after interacting with another ball or with the edge of the table. So, the physical quantity which measures this variation of linear momentum is called an impulse.

Conservation of linear momentum 

There might be a situation where all the balls in the table will be moving at the same time. The sum of the linear momenta of each ball constitutes the linear momentum of the system. As you know, linear momentum is a vector. So the linear momentum of each ball must be taken as vector, while adding. Suppose, there exists a situation when few balls collide, some balls can accelerate while other balls can decelerate, then what happens to the linear momentum of the system? Try to find the mass and speed of the balls before collision and try to detect the speed of any one of the ball after interaction.

Conclusion about linear momentum and impulse

 I have defined linear momentum and impulse. So when the linear momentum of a body is increased then it is receiving positive impulse, whereas when the linear momentum of the body is decreased, then it is receiving negative impulse. Principle of conservation of linear momentum: that total linear momentum of system remains constant when the system does not receive any external impulse.

Elastic collision

There might be some energy lost into the environment when two bodies collide. There might be some heat loss or energy wasted which can be neglected. The collision is considered elastic if the total kinetic energy remains conserved. In this case the linear momentum and kinetic energy are used to determine the velocity of each particle after the collision. Not all the collisions are elastic in nature. In certain cases the variation of energy are so small that it is very hard to detect, such cases are also considered as elastic collisions.

 Completely inelastic collision 

the loss of energy is maximum and cannot be neglected the collision is set to be inelastic. For example a bullet shot on a block of wood.

 A real collision 

 it is needed elastic nor completely inelastic. There is a coefficient K, which is called as coefficient of restitution. This measures the degree of elasticity. It can take values from 0 to 1. There is another coefficient called as impact coefficient which also takes values from 0 to 1. Change of these two parameters explains any type of collision occurring between two bodies.

 Conclusion 

there are two cases in which it is possible to determine how a particle will move after collision. Frontal elastic collision in which both kinetic energy and linear momentum are conserved. Completely inelastic collision where both the particles remained stuck to each other even after collision. This case results maximum loss of energy. Real collision is determined by the coefficient of restitution. This will oscillate in between frontal elastic collision and completely inelastic collision