A train locomotive is pulling two cars of the same mass behind it, Fig. 4–51. Determine the ratio of the tension in the coupling (think of it as a cord) between the locomotive and the first car ($F_\textrm{T1}$), to that between the first car and the second car ($F_\textrm{T2}$), for any nonzero acceleration of the train.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Let's consider what this tension force 1 is pulling. As this is the coupling between the engine and car 1, it's pulling this total mass of 2m, it's pulling both the cars. And you can consolidate these two masses into an imagined single block of mass, 2m, and the net force on this combined system, you combine the two cars into one is just FT1, it's the only force on it. And so, that means it equals the mass times acceleration, and the mass is 2m times acceleration a. And if you consider the coupling that's linking car 1 to car 2, it has to pull a mass of only m. And it is the net force and so it equals the mass times acceleration and the mass is only m times a. And so we have expressions for each of these coupling forces now, and so let's divide them to find the ratio. So, FT1 divided by FT2 is 2ma over ma, and that equals 2. So, the ratio of the forces is 2.