Mass and Momentum, Momentum and Newton՚s Second Law, Impulse (For CBSE, ICSE, IAS, NET, NRA 2022)

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Mass and Momentum

About Mass

  • Mass is the inherent property of matter. It is the measure of the inertia of a body, mass tells us how much matter there is in a body, we can measure the mass of a body on earth by measuring the force of gravity acting on it, the SI unit of mass is kilogram (kg) .
  • Keep in mind that, mass is not the same as weight, even though we measure the mass of a body by measuring its weight, a body with the same mass weighs differently on the moon than it weighs here on earth, mass is one property of matter that doesn՚t change easily.
  • Mass is a form of energy; it is energy at rest.
  • In 1905 Albert Einstein formulated the theory of special relativity;

  • Which states that energy is mass times the speed of light,
  • That՚s a lot of energy inside just 1 kilogram of matter, this energy can be tapped by recent advancements in nuclear technology and by means of nuclear fission, and a small amount of matter is converted into clean energy.

About Momentum

  • Inertia is the property of mass that resists change.
  • Momentum is defined as the quantity of motion of the body.
  • It is measured by mass times velocity, as momentum depends upon velocity, and it depends on the direction of the motion of the body as well.
  • Momentum is a vector quantity since velocity is vector while mass is scalar.
  • It is safe to say that as the mass of an object increases so does its inertia.
  • Weight is the measurement of resting inertia and momentum is the measure of inertia at a certain velocity.
  • We all know that at the same forward velocity it would be harder to stop a rolling car that a rolling bike.

Unit of momentum is given as:

Unit of Momentum
SI unitkg.

The law states that the total momentum of a closed system does not change, which means that if two bodies collide with each other, their total momentum after the collision will be equal to their momentum before the collision.

Momentum and Newton՚s Second Law

  • The importance of momentum was recognized early in the development of classical physics.
  • Momentum was deemed so important that it was called the “quantity of motion.”
  • Newton stated his second law of motion in terms of momentum: The net external force equals the change in momentum of a system divided by the time over which it changes.
  • Using symbols, this law is

where

  • is the net external force,
  • is the change in momentum,
  • is the change in time.

Impulse

At constant velocity the momentum of an object remains constant but if that object comes in contact with another object there is a change in momentum that is related to the time of contact. This relationship is called impulse.

The way that the knowledge of impulse becomes useful is in the application of time. The longer it takes to change the momentum, the less force is exerted on an object and vice-a-versa.

If the breaks are applied to a running train gently, the momentum of the car is changed gradually over a long period of time and the force on you the passenger is slight. If you STOMP on the breaks, the momentum of the car changes immediately and the force on the passenger is great. The impulse is the same for the two situations but the time and force are different.

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