Example:
A freight train is being assembled in the switching yard, and the figure above shows twp boxcars. Car 1 has a mass of m1 = 65 . 103 kg and moves at a velocity of V01 = +0.80 m/s. Car 2, with a mass of m2 = 92 . 103 kg and velocity of V02 = +1.3 m/s, overtakes car 1 and couples to it. Neglecting friction, find the common velocity Vf of the cars after they become coupled.
Reasoning: The two boxcars constitute the system. The sum of the external forces acting on the system is zero, because the weight of each car is balanced by a corresponding normal force, and friction is being neglected. Thus, the system is isolated, and the principle of conservation of momentum applies. The coupling force that each car exerts on the other are internal forces and do not affect the applicant of this principle.
Solution: Momentum conservation indicates that
The equation can be solved for Vf, the common velocity of the two cars after the collision:
