Conservation of momentum

Question 1 State the law of conservation of mass?

Question 2 Discuss the conservation of momentum in a rocket taking off from the ground?

Question 3 A 60 g bullet fired from a 5 kg gun leaves with a speed of 500 m/s.Find the speed with which the gun recoils?

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