# Explosions and Momentum

Common examples of the conservation of momentum center around two or more objects colliding in the absence of external forces.  Another twist on the example of a collision would be the idea of a reverse collision or an explosion.  If you video tape an explosion and play it backwards, it looks like a collision.   Likewise, if you video tape a collision and play it backwards it resembles an explosion.

If we look at the case of a canon being fired, we find there is a force of the gun powder exploding creating a force of the canon pushing on the cannon ball and the cannon ball pushing back on the gun.  These two forces are equal in size but opposite in direction.  If any forces that are external to the cannon-&-ball system (such as weight and friction) are removed.  Then momentum must be conserved.

 In the example at the left, the external forces have been removed by placing the cannon on a frictionless surface.  in the beginning, both the cannon and the ball are at rest.  As a result, the total momentum before the explosion is 0.   Since the total momentum of an isolated system (means no external forces) is conserved, then the total momentum after the explosion would also be zero.

Mathematically this explosion would look like:

You will notice that the cannon has a new velocity that is in the opposite direction of the velocity of the cannon ball.  Remember, momentum is conserved, not velocity.  So the mass of the cannon ball is 20 times smaller than the mass of the cannon, as a result  the velocity of the cannon ball is 20 times larger!   Consider what would happen if you had a cannon with a small mass and a ball with a large mass.

This concept of momentum being conserved in an explosion is true for an explosion along a line (1 dimensional as in the animation), an explosion along a plane (2-D), or an explosion in free space (3D) for something like a hand grenade.