MOMENTUM
🅸ntroduction
If we throw two stones of equal mass with different velocities, we observe that the effect of motion,they have, are different. Similarly, if two stones of different mass be thrown with a same velocity, the effect of motion, they possess ,are also different. Here, the property which brings difference in the effect of motion, in the language of science, it is termed as Momentum.
Here, we will learn momentum, its definition, mathematical and graphical representations, types, relation with energy , law of conservation of momentum, application and some problems with explanation.
What is momentum?
Magnitude of motion is called momentum. Momentum is measured by the product of mass and velocity of an object.
i.e momentum = mass x velocity
or, p = mv
Unit of momentum :-
As, p = m x v
therefore, SI unit of momentum = unit of m x unit of v
= kg x ms-1 = kgms-1
Momentum is vector quantity
As, p = mv
, Here m is scalar but v is a vector. Hence , the product of scalar and a vector is a vector. So, momentum is a vector.
Direction of momentum is same as the direction of velocity.
Momentum is a useful quantity
In dynamics, momentum is very useful . The study of Newton's law of motion is based on momentum. Many phenomena are explained on the basis of momentum.
GRAPHICAL REPRESENTATION
Principle of Conservation of momentum
According to this principle,
The total momentum of an isolated system remains constant.
or,In the absence of external force, the total momentum of a system of particles remains conserved. The total linear momentum is the vector sum of the linear momenta of all the particles of the system.
Here, we should notice that the momentum of an individual particle of a system may change, but the total momentum ,i.e., the sum of momenta of the constituting particles of a system remains constant.
Types of momentum
Two types of momenta are
1. Linear momentum or momentum (p)
It is the product of mass (m) and linear velocity (v) of a particle or a system . It is generally used for rectilinear motion.
2. Angular momentum (L)
It is used in rotational motion.It is defined as the moment of momentum and is given as
L = r × p = mvr
Momentum and Kinetic energy
Using this expression, what will be the expression of P ?
Practical applications based on the law of conservation of momentum
1. Recoil of a gun:
The gun and a bullet inside it , constitute a system.
Let,
M = Mass of the gun
m = Mass of the bullet
Before firing, both the gun and the bullet are at rest. After firing, the bullet moves with velocity V₁ and the gun moves with velocity V₂ .
As no external force acts on the system , so according to the principle of conservation of momentum,
Total momentum before firing = Total momentum after firing
0 = mV₁+M V₂
M V₂ = - mV₁
V₂ = -(m/M) V₁
The negative sign shows that V₁V₂ are in opposite directions, i.e. , the gun gives a kick in the backward direction or the gun recoils with velocity V₂.
2. Working of Rocket and Jetplanes
Initially, the rocket and its fuel are at rest. So, their total momentum is zero. For rocket propulsion, the fuel is exploded. The burnt gases are allowed to escape through a nozzle with a very high downward velocity. The gases carry a large momentum in the downward direction. To conserve momentum, the rocket also acqires an equal momentum in the upward direction and hence starts moving upwards.
3. Astronaut in open space
An astronaut in open space, who wants to return to the spaceship, throws some object in a direction opposite to the direction of motion of the spaceship. By doing so, he gains a momentum equal and opposite to that of the thrown object and so he moves towards the spaceship.
4. While firing a bullet, the gun should be held tight to the shoulder
The recoiling gun can hurt the shoulder. If the gun is held tightly against the shoulder, then the body and the gun together will constitute one system. Total mass becomes large and the recoil velocity becomes small.