Overview – Momentum and Collisions

Momentum

• Momentum is defined as a quantity of movement of the body.
• It is measured by mass times velocity (mass × velocity).
• Momentum depends upon velocity, and it also depends upon the direction of the moving body.
• Momentum is a vector quantity (quantity which has both direction as well as magnitude), since velocity is vector quantity while mass is scalar quantity (quantity which has only magnitude).
• In terms of equation momentum can be written as:

p = mv

where, p = momentum

            m = mass

            v = velocity

So, Momentum = Mass X Velocity

• By looking at above equation it tells two things, first, that momentum is directly proportional to the mass of any object and second, it is directly proportional to the velocity of that object.
• The SI unit of Momentum is kg.m.s^-1
• Momentum can also be described as "mass in motion." As all the objects have mass so, if an object is moving, then it definitely has some momentum.
• It is also said that momentum is another measurement of the vector. Momentum and the velocity are both in the same direction
• Simple examples of momentum are walking and running.
• There is also a law of conservation of momentum, which states that the total momentum of a closed system does not change, if the two bodies are collided with each other, then the total momentum of the same two bodies after the collision will be equal to the momentum before the collision.
• Mathematically we can say,

 +  =  +  

where, m = mass

               u = initial velocity

               v = final velocity

             m₁ = Mass of 1st body

              m₂ = Mass of 2nd body

               u₁ = Initial velocity of 1st body

               u₂ = Initial velocity of the second body

               v₁ = Final velocity of the first body

               v₂ = Final velocity of the second body

• Total momentum remains constant if any external force does not act on the system in an isolated system.
• The law of conservation of momentum is based on Newton’s third law of motion which states that “every action is equal and opposite reaction”.

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Collision

• Collision means two objects comes in contact of each other.
• Or we can say collision is a counter interaction between two masses for a very short interval of time.
• It can also be defined as the event in which two or more bodies exert forces on each other for relatively short interval of time.
• There are two types of collision:

1. Elastic collision: It is defined as when two bodies collide with each other but there is no loss in the overall kinetic energy, it is called a perfectly elastic collision.

• We can also say in elastic collision there is no net loss in kinetic energy of the system due to the collision.
• The kinetic energy before the collision of two or more bodies and after the collision remains the same. It is not converted into other forms of energy in case of elastic energy.
• Momentum and the kinetic energy, both are conserved in elastic collision.
• Example of elastic collision is swinging balls.

2. Inelastic Collision: In this type of collision, the bodies stick to each other or move in the same direction.

• The total kinetic energy in inelastic collision is not conserved but the total momentum and energy are conserved.
• In inelastic collision the energy is transformed into other energy forms like heat and light.
• Or we can say that in inelastic collision there is a loss of kinetic energy and the lost kinetic energy is being transformed into either in the thermal energy or sound energy, and sometimes in material deformation.
• Examples of inelastic collision is collision of two cars.