Two-color Train

A train consists of a locomotive, pulling 100 yellow cars, which in turn pull 200 blue cars. The train travels on a level track, accelerating forward at rate aa.

Each yellow car has 3 times as much mass as a blue car.

The cars experience rolling friction opposing the motion: Ff=μmgF_f = \mu m g, where mm is the mass of the car, μ=0.10\mu = 0.10 for yellow cars, and μ=0.20\mu = 0.20 for blue cars.

Let FLYF_{LY} be the force exerted by the locomotive on the first yellow car, and FYBF_{YB} the force by the last yellow car on the first blue car.

If FYB=12 FLYF_{YB} = \tfrac12\ F_{LY}, how fast does the train accelerate? Give your answer as the ratio ag\frac{a}{g}.


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