In completely inelastic collisions, the objects involved stick together and move as one mass after the collision. The equation governing this process is m1v1 + m2v2 = (m1 + m2)v', where m1 and m2 are the masses and v1 and v2 are their velocities before the collision, with v' representing their common velocity afterward. This scenario illustrates the law of conservation of momentum, which states that the total momentum of a closed system remains constant before and after the collision. However, kinetic energy is not conserved in these collisions, as some energy is transformed into other forms, such as heat and sound. Understanding these principles is crucial for analyzing momentum in physics.