Head-on Collision of Unequal Masses

Main Idea

The two main types of collisions are elastic and inelastic collisions, but these are very broad as there are many much more specific types of collisions under these umbrella terms. One of the specific types of collisions is head-on collisions of unequal masses. This is exactly what it sounds like - two objects of different masses collide with each other head-on, and this causes some changes in kinetic energy and speed. This can be thought of as two different types of cars colliding with each other, but to make the visualization a bit easier, think about a ping pong ball colliding with a bowling ball.

Elastic head-on collision between a car and truck

The Equations Behind It

The most common type of head-on collision of unequal masses studied is an elastic collision, and if this is the case kinetic energy is conserved. What this means is that the total final kinetic energy of the system is equal to the total initial kinetic energy of the system. In equations, it looks like this: [math]\displaystyle{ {1 \over 2}m_1v_1i^2 + {1 \over 2}m_2v_2i^2 = {1 \over 2}m_1v_1f^2+ {1 \over 2}m_2v_2f^2 }[/math].

If the equation is inelastic, the idea of conservation of momentum can be used because momentum is always conserved in collisions. The equation for the conservation of momentum is: [math]\displaystyle{ m_1v_1i^2 + m_2v_2i^2 = m_1v_1f^2 + m_2v_2f^2 }[/math]