# Funicular Railway

Pro Problems > Physics > Motion and Forces > Linear Motion > Force > Friction > Static Friction## Funicular Railway

A funicular is a train with two cars attached by a rope/chain. The two train cars are on parallel tracks on the side of a mountain. While one car is at the top, the other is at the bottom. In order to reverse position, water is pumped into a tank in the car at the top until it is heavier than the car at the bottom. Then, when the brakes are released, the top car pulls the bottom car up as it goes down. Once they have reversed positions, the water is drained from the lower car's tank, and the process can be reversed.

There is a very small coefficient of rolling friction between each car and the track (0.0005). We will assume the system is otherwise frictionless.

Both cars have a mass of 50,000 kg. The car at the top of the mountain has 30 passengers, with an average mass of 75 kg. The bottom car has 25 passengers with an average mass of 80 kg.

If the slope of the track is 30 degrees, how much water will be needed in the top car to set the apparatus in motion?

## Solution

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