# 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