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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