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 Example : 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

                              Acceleration of car (a) =  (v₂ – u₂₎ / t                                  

F = m x a

F₁  = Force exerted by truck on the car

F₁ = m₂ x  (v₂ – u₂) / t

Acceleration of truck = (v1 – u1) / t

F₂  =   m₁  x  (v₁ – u₁ ) / t

F₁ = – F₂

m₂  x (v₂ – u₂ )/ t = – m₁ x (v₁ – u₁ )/ 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