1. The problem statement, all variables and given/known data A locomotive accelerates a 34-car train along a level track. Every car has a mass of 6.2 × 104 kg and is subject to a frictional force f = 165v, where the speed v is in meters per second and the force f is in newtons. At the instant when the speed of the train is 31 km/h, the magnitude of its acceleration is 0.11 m/s2. (a) What is the tension in the coupling between the first car and the locomotive? (b) If this tension is equal to the maximum force the locomotive can exert on the train, what is the steepest grade up which the locomotive can pull the train at 31 km/h? 2. Relevant equations F=ma V was converted to m/s (Force of locomotive) = (34)(62000)(0.11) <-------total mass of the system includes all 34 cars (frictional force) = (0.11)(34) <-----since friction is acting on each individual car 3. The attempt at a solution Okay, found an internet guru that said that: (Tension) = (Force of locomotive) + (frictional force) Using this equation, the tension was found. What I don't understand is. Why? First off, moving the friction force to the left of the equation using algebra we get that: (Tension) - (frictional force) = (Force of locomotive) What's confusing about this is that the Tension should be acting against the pull of the locomotive, which is what the friction is doing as well, so why aren't they added? Perhaps I am misunderstanding what forces are where and how they work? What am I missing? I've found the answer already, but I want to understand WHY. WHY. Y. Hahahah, seriously though, any help would be appreciated.