Explain conservation of momentum.

Conservation of Momentum

When two or more bodies act upon one another,their total momentum remains conserved provided no external force acts on them.

For Ex:When a speeding truck hit a stationary car due to which the  car also start moving.

The momentum lost by truck is gained by car.
Momentum can neither be created nor destroyed .
Let us consider a truck and car are moving in same direction but with different speeds.

Total momentum=m₁u₁ + m₂u_{2
Suppose the car and truck collide for a short time t , their velocities will change.}
 

Total Momentum = m₁v₁ + m₂v₂
                                 

                                       v₂ – u₂

Acceleration of car (a) =  ————-

                                            t

F = m * a

F₁  = Force exerted by truck on the car

F₁ = m_{2 *}   (v₂ – u₂)

       ———————

                     t

                                   v₁ – u₁      

Acceleration of truck =————

                                     t

F₂  =   m₁  * (v₁ – u₁ )

          ———————

                        t

F₁ = – F₂

m₂  * (v₂ – u₂ )             –    m₁ * (v₁ – u₁ )

——————–  =         —————–

                t                               t

m₂  (v₂ – u₂ ) = – m₁ * (v₁ – u₁ )

m₂  v₂  – m₂ u₂  = – m₁ v₁   + m₁ u₁

m₂  v₂  + m₁ v₁ = m₁ u₁ + m₂ u₂

or

m₁ u₁ + m₂ u₂  = m₂  v₂  + m₁ v₁