Force and Laws of Motion

CONSERVATION OF MOMENTUM

• The law of conservation of momentum states that: When two (or more) bodies act upon one another, their total momentum remains constant (or conserved) provided no external forces are acting on them.
• This law can also be stated as: Momentum is never created or destroyed.
  i.e.  
  $m_1{u}_1 + m_2{u}_2 = m_1{v}_1 + m_2{v}_2$

  Total momentum before collision=Total momentum after collision

• Conservation is only true for system. Because if we consider only a single body or , then net force will be acting on it so we cannot represent the body as:
  $m_1{u}_1 \ne m_1{v}_1 or m_2{u}_2 \ne m_2{v}_2$

  or .

APPLICATION OF THE LAW OF CONSERVATION OF MOMENTUM

Gases through the tail nozzle of the rocket move in the downward direction with tremendous speed or velocity. In order to balance the momentum of the gases, the rocket moves up. Though the mass of gases emitted is comparatively small, they have a very high velocity and hence a very large momentum. An equal momentum is imparted to the rocket in the opposite direction, so that, despite of its large mass, the rocket goes up with a high velocity.