Tension of Cable Cars in San Francisco's Cable System

[wafflehouse]

The cable cars in San Francisco are pulled along their tracks by an underground steel cable that moves along at 9.5 mph. The cable is driven by large motors at a central power station and extends, via an intricate pulley arrangement, for several miles beneath the city streets. The length of a cable stretches by up to 100 ft during its lifetime. To keep the tension constant, the cable passes around a 1.5-m-diameter "tensioning pulley" that rolls back and forth on rails, as shown in the figure. A 2000 kg block is attached to the tensioning pulley's cart, via a rope and pulley, and is suspended in a deep hole.

What is the tension in the cable car's cable?

 

[Nate810]

The tension in the cable car's cable is equal to the weight of the block, which is 2000 kg, multiplied by the acceleration due to gravity, which is 9.8 m/s2. Therefore, the tension in the cable car's cable is 19,600 N.

 

[ogb p]

I would first need to gather more information about the specific cable car system in San Francisco in order to accurately calculate the tension in the cable. This would include the weight of the cable car, the angle of the cable as it passes around the tensioning pulley, and the specific materials and dimensions of the cable and pulley system.

However, I can provide some general insights about the tension in the cable based on the given information. Since the cable car is pulled by an underground steel cable, we can assume that the tension in the cable is relatively high in order to support the weight of the cable car and any passengers. The fact that the cable stretches up to 100 ft during its lifetime also suggests that the tension in the cable is constantly changing and needs to be carefully managed.

The use of a tensioning pulley and a 2000 kg block to maintain constant tension in the cable is a common technique used in cable systems. The weight of the block and the force exerted by the cable passing around the pulley can be used to calculate the tension in the cable. However, this calculation would require more information about the specific system.

Overall, the tension in the cable car's cable is a crucial factor in ensuring the safe and efficient operation of the cable car system. It is important for engineers and technicians to carefully monitor and manage the tension in the cable to ensure the smooth movement of the cable cars and the safety of passengers.