Two-color Train

Classical Mechanics Level 3

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 $a$ .

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

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

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

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

The answer is 0.10.

1 solution

Arjen Vreugdenhil
Oct 8, 2016

Let $m$ be the mass of a single blue car. In order for 200 of these cars to accelerate at rate $a$ , they must be pulled by a force $F_{YB} = F_{net,B} + F_{f,B} = 200ma + 40mg.$ Likewise, treating the yellow and blue cars together as a single system pulled by the locomotive, we have $F_{LY} = F_{net,sys} + F_{f,sys} \\ = (300m + 200m)a + (30mg + 40mg) = 500ma + 70mg.$

The given ratio implies that $2(200ma + 40mg) = 500ma + 70mg \\ 10mg = 100ma \\ a = \boxed{0.1}\ g.$

good ques Arjen sir !

A Former Brilliant Member - 4 years, 8 months ago

Two-color Train

The answer is 0.10.

1 solution

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