Principle of Conservation of Momentum

Example – Both Objects are in the Same Direction before Collision
A Car A of mass 600 kg moving at 40 ms^-1 collides with a car B of mass 800 kg moving at 20 ms^-1 in the same direction. If car B moves forwards at 30 ms^-1 by the impact, what is the velocity, v, of the car A immediately after the crash?
Answer:
m₁ = 600kg
m₂ = 800kg
u₁ = 40 ms^-1
u₂ = 20 ms^-1
v₁ = ?
v₂ = 30 ms^-1

According to the principle of conservation of momentum,

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
(600)(40) + (800)(20) = (600)v₁ + (800)(30)
40000 = 600v₁ + 24000
600v₁ = 16000
v₁ = 26.67 ms^-1

Example – Both Object are in opposite direction Before Collision
A 0.50kg ball traveling at 6.0 ms^-1 collides head-on with a 1.0 kg ball moving in the opposite direction at a speed of 12.0 ms^-1. The 0.50kg ball moves backward at 14.0 ms^-1 after the collision. Find the velocity of the second ball after collision.

Answer:
m₁ = 0.5 kg
m₂ = 1.0 kg
u₁ = 6.0 ms^-1
u₂ = -12.0 ms^-1
v₁ = -14.0 ms^-1
v₂ = ?

(IMPORTANT: velocity is negative when the object move in opposite direction)

According to the principle of conservation of momentum,

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
(0.5)(6) + (1.0)(-12) = (0.5)(-14) + (1.0)v₂
-9 = – 7 + 1v₂
v₂ = -2 ms^-1

Example:
A man fires a rifle which has mass of 2.5 kg. If the mass of the bullet is 10 g and it reaches a velocity of 250 m/s after shooting, what is the recoil velocity of the pistol?
Answer:
This is a typical question of explosion.

m₁ = 2.5 kg
m₂ = 0.01 kg
u₁ = 0 ms^-1
u₂ = 0 ms^-1
v₁ = ?
v₂ = 250 ms^-1

By using the equation of conservation of momentum principle
0 = m₁v₁ + m₂v₂
0 = (2.5)v₁ + (0.01)(250)
(2.5)v₁ = -2.5v₁ = -1 ms^-1