Types of Collisions and Conservation of Momentum

Ever wonder what happens when two cars crash or billiard balls collide? In physics, we classify collisions into three main types. In a perfectly inelastic collision, objects stick together after colliding, moving as one mass. The equation $M_1V_1 + M_2V_2 = M_{12}V$ helps us calculate their final velocity.

In a regular inelastic collision, objects deform during impact and lose kinetic energy, but continue moving separately afterward. Despite this energy loss, momentum remains conserved, following $M_1V_1 + m_2V_2 = m_1v_1 + m_2v_2$.

A perfectly elastic collision occurs when objects bounce off each other with no energy loss—like a ball bouncing back to its original height. All other real-world collisions fall somewhere in between, being partially elastic. For explosions, which are like collisions in reverse, we use $m_{Total}V = m_1V_1 + m_2V_2$.

Remember This! The principle of conservation of momentum works because of Newton's Third Law—during a collision, the impulse (and therefore momentum change) experienced by one object equals the opposite impulse experienced by the other.

Let's see this in action with examples: When an 8,000 kg train car moving at 10 m/s collides with a stationary 2,000 kg car and they stick together, their final velocity is 8 m/s. For two colliding billiard balls in an elastic collision, we can calculate that if one rebounds at 0.4 m/s, the other must move at -0.606 m/s to satisfy conservation of momentum.