Question

CONSERVATION OF MOMENTUM

DERIVATION WITH EXAMPLE

Answer 1

Firstly You must know about the Term Momentum...

Momentum is a physical quantity....which is actually a Effect of Motion...Any Body having mass m and Velocity v must have momentum...Even body having no mass also have momentum...which you will study in your higher classes...

Momentum of any body can be calculated by the product of mass and velocity....It is denoted by letter P...

P = m x v

Momentum is a vector quantity whose direction is along the direction of velocity...and its unit is Kgm/s...

Here conservation means Constant....Momentum is conserved means Total initial momentum must be equal to total Final momentum....

The explosion of bomb is due to conservation of momentum...if momentum wont conserve in this situtation..bomb will not explode at all...

Lets understand this with an example :

Suppose the mass of Canon is M=1000kg and mass of canon ball is m=50kg say..

Initial velocity of Canon = u1
Final Velocity of Canon = v1

Initial velocity of Canon ball = u2
Final velocity of Canon Ball = v2


...Initially both Canon and ball are at rest...so their initial velocities are 0...
Before Fire...
Initial momentum of Canon = M x u1= M x 0 = 0 kgm/s
Initial momentum of Canon ball = m x u2 = m x 0 = 0 kgm/s..

Total Initial Momentum of the system( Canon + Canon ball) (before fire) = 0 + 0 = 0 kgm/s

After fire...
In this Situation Both Canon and canon ball have Some velocities in opposite Direction..lets suppose the velocities as...
V1 ( Final velocity of Canon) = - 5m/s say ( negative sign shows that velocity is in the opposite direction)
V2(Final Velocity of Canon Ball) = + 100m/s

Final momentum of Canon = M x V1 = 1000 x (-5) = -5000 kgm/s
Final momentum of Canon Ball = m x V2 = 50 x 100 = 5000kgm/s..

Tota Final(After fire) momentum of the System (Canon + Canon ball) = -5000 + 5000 = 0 kgm/s..

Here you can see..
Total initial momentum Of the system = Total final momentum of the system = 0...Hence momentum is conserved...

Simillarly During explosion..Bomb particles go in different directions...If we calculate the initial and final momentum of each particles...we will find the momentum is conserved....

If momentum will not conserve..then bomb will not explode..it will go in particular direction...

Simply...the conservation of Momentum or Momentum is conserved only if..

Total initial momentum of the system = Total Final momentum of the system..

hope this help...

Answer 2

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Conservation 0f Momentum➫ A system in which the momentum of a system is constant if there are no external forces acting on the system.

Prove: Conservation 0f Momentum:-▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃⤵

➧Let the Body A = m1 & B = m2

➧Let their velocity be u1 & u2
(u1 > u2)

➧Momentum of Body
A = m1u1 & B = m2u2

❱ Initial & Final momentum of System
➾ m1u1 + m2u2

◉ Body A exert force of Action
➾ Fᴀʙ on Body B.

◉ Body B exert force of Reaction
➾ Fʙᴀ on Body A.

▸ Fᴀʙ = Body A
➾ m1 (v1 - u1) / t

▸ Fʙᴀ = Body B
➾ m2 (v2 - u2) / t

▸ Since, Action = - reaction
▸ So, Fᴀʙ = - Fʙᴀ

m1 (v1 - u1) / t = - m2 (v2 - u2) / t

▸ m1v1 - m1u1 = m2v2 + m2u2
▸ m1v1 - m2v2 = m1u1 + m2u2...✔

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Thanks...✊