Table of Contents
Introduction:
The momentum is a very important quantity since it is conserved. Though it was not conserved in the examples taken in the impulse and the linear momentum and in the force, where the large changes in the momentum were produced by the forces acting on the system of interest.
The momentum is always equal to the mass of an object when multiplied by its velocity and is equivalent to the force required to bring the object to a stop in a unit length of the required time. For an array of several objects, the total momentum is the sum total of the individual momentum. Sometimes the momentum is a vector containing both the direction and the magnitude of motion so that the momentum of objects going in the opposite directions can cancel to yield an overall sum of zero.
The example of the conservation of momentum is as follows: Consider the example of a balloon, the particles of gas move rapidly by colliding with each other and with the walls of the balloon. Even though the particles themselves move faster and slower when they lose or gain momentum or when they collide. Still in the total momentum of the balloon system there is no change. Therefore the balloon doesn’t change in size. If we add external energy by providing heat to it, the balloon should expand because it increases the velocity of the particles and this increases their momentum and increases the force exerted by them on the walls of the balloon.
A brief outline of the topic:
The conservation of momentum is the concept of physics along with the explanation of conservation of energy and the conservation of mass. The momentum is described to be the mass of an object multiplied by the velocity of the object. According to the conservation of momentum, the amount of momentum does not change and remains constant within some problem domains.
The momentum is neither created nor be destroyed but can only be changed through the action of forces as stated by Newton’s laws of motion. Sometimes dealing with the momentum is more difficult than dealing with mass and energy since the momentum is a vector quantity with both a magnitude and a direction.
The momentum is conserved in all three physical directions at the same time. It is even more difficult when it deals with the gas because all the forces in one direction can affect the momentum in another direction due to the collisions of many molecules. This problem is further simplified by considering a steady flow that does not change with time and by limiting the forces to only those associated with the pressure.
A brief note of important concepts and laws:
The total momentum of a rocket and its fuel is zero before launching. During the launch, the downward momentum of the expanding exhaust gasses is almost equal in magnitude to the upward momentum of the rising rocket. Therefore the total momentum of the system does not change hence remains constant at zero value. In a collision of two particles, the sum of the two momentum before the collision is almost equal to their sum after the collision.
The law of conservation of momentum is particularly confirmed by the experiment and can even be mathematically derived on the reasonable assumption that the space is uniform. This means that there is nothing in the laws of nature that singles out one position in space as peculiar when compared with any other.
There is a similar conservation law for the angular momentum which describes the rotational motion in the same way that the ordinary momentum describes the linear motion. Additionally, the mathematical expression of this law is more involved. There are numerous examples of this. In every helicopter, there is a requirement of at least two propellers for stabilization. The body of a helicopter can be able to rotate in the opposite direction to conserve the angular momentum if there were only a single horizontal propeller on the top. According to the conservation of the angular momentum, the ice skaters can spin faster as they pull their arms toward their body and more slowly as they extend them.
The angular momentum conservation has also been explained by several experiments and can be shown to follow mathematically from the reasonable assumption that space is uniform with respect to orientation.
Mathematically it is given by,
m 1 u 1 + m 2 u 2 m 1 u 1 + m 2 u 2 =m 1 v 1+m 2 v 2 m 1 v 1+ m 2 v 2
In the above mentioned equation,
m 1= mass of the bowling ball
m 2= is the mass of the football
u 1 and u 2 = the initial velocities
v 1 and v 2 = the final velocities
In short, the momentum is always conserved in any collision whether it is elastic or a non-elastic collision. The kinetic energy is not conserved in a non-elastic collision; the kinetic energy is converted into heat energy or potential energy.
Also read: Conservation of Mechanical Energy
FAQs (Frequently Asked Questions):
Que: State the law of conservation of momentum.
Ans: The law of conservation of momentum states that in an isolated system the total momentum of two or more than two bodies acting upon each other does not change and remains constant until an external force is applied. Thus momentum can neither be created nor destroyed.
Que: Mention the real-life example of the law of conservation of momentum?
Ans: The nervousness thrust that you feel during the time of firing is one of the real-life examples of the conservation of momentum.
Que: Give the formula of the law of conservation of momentum.
Ans: The formula of the law of conservation of momentum is given as follows:
m 1 u 1 + m 2 u 2 =m 1 v 1 + m 2 v 2
In the above equation,
m 1 and m 2= are the masses of the bodies
u 1 and u 2 = are the initial velocities of the body
v 1 and v 2 = the final velocities of the bodies.
Que: Does friction affect the conservation of momentum?
Ans: Yes, the friction affects the momentum as the friction increases and the momentum decreases.
