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.

         Truck            Car
         Velocity      Decreases         Increases
       Momentum      Decreases         Increases

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.

        Truck       Car
Mass         m1      m2
Velocity         u1       u2
Initial Momentum        m1u1      m2u2

Total momentum=m1u1 + m2u2
Suppose the car and truck collide for a short time t , their velocities will change.

        Truck       Car
Mass         m1      m2
Velocity         v1      v2
Final Momentum          m1v1      m2v2


Total Momentum = m1v1 + m2v2

                                 

                                       v2 – u2

Acceleration of car (a) =  ————-

                                            t

F = m * a

F= Force exerted by truck on the car

F1 = m2 *   (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 )

mv2  – m2 u2  = – m1 v1   + m1 u1

mv2  + m1 v1 = m1 u1 + m2 u2

or

m1 u1 + m2 u2  = mv2  + m1 v1

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