Momentum conservation

Momentum is conserved in a collision or explosion in an isolated system where no external forces act. In other words the momentum before the collision or explosion is the same as that after it. This is true for ALL collisions and explosions Consider a cannon at rest firing a shell.

Momentum before explosion = Momentum after explosion = 0 = MV+mv

where M and V are the mass and velocity of the cannon and m and v are the mass and velocity of the shell. So V = - mv/M, the minus sign meaning that the cannon is moving in the opposite direction to the shell. (Remember that momentum is a vector)

In a collision the same law of conservation of momentum applies. If a mass m₁ moving at a velocity u₁ collides with a mass m₂ moving at a velocity u₂ such that after the collision m₁ moves at v₁ and m₂ moves at v₂ then:-

momentum before collision = momentum after collision m1u1 + m2u2 = m1v1 + m2v2