We went up the funicular railway on Cairngorm Mountain for the first time in a decade. It was the last weekend of the ski season. The ski station is in the top left hand corner of the first picture. It is 453 metres higher than the bottom station. There are two carriages on the railway and they are tied together by a steel cable. When one goes up, the other goes down. In the bottom photograph you can see that there is a short section in the middle where they can pass each other. In an ideal, frictionless world, no energy would be needed to move two carriages of equal mass. The gravitational potential energy lost by the one going down would be transferred to the one going up. The maximum load is 120 passengers. Let's consider a situation where the carriage going up is full of passengers but the one going down is empty. The falling carriage cannot provide all of the energy needed to raise the other carriage with passengers so a motor is needed to pull on the cable that joins the carriages. 120 passengers at say 60kg each is 7200kg. By mgh, it needs 32,600,000J of energy to raise them to the top station. The fastest journey takes 4 minutes. 32,600,000 / 240 seconds = 134kW. This is much lower than the stated 1000kW operating power of the motor. Ah, but we assumed no friction ...
