What Is the Tension in San Francisco's Cable Car System?

In summary, the cable cars in San Francisco are powered by an underground steel cable that runs at 9.5 mph and is driven by large motors. To maintain tension, the cable passes around a 1.5-m-diameter "tensioning pulley" that rolls back and forth on rails. The tension is kept constant by a 2000 kg block attached to the pulley's cart via a rope and pulley. The forces acting on the cart and pulley system are the tension of the hanging mass, the normal force of the rail on the cart, and the tension from the rope in the pulley.
  • #1
accobos
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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?T[tex]_{b on a}[/tex]=T[tex]_{a on b}[/tex]

I just don't even know where to start. I know that it's not accelerating, so Net Force=0 but I still can't figure out where to go from here. If I could just get pointed in the right direction, that'd be great! Thanks so very much!
 

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  • #2
Hint: Treat the cart and pulley as a single system. What forces act on it?
 
  • #3
The tension of the hanging mass and the normal force of the rail on the cart, and the tension from the rope in the pulley?
 

FAQ: What Is the Tension in San Francisco's Cable Car System?

1. What is tension in a cable car's cable?

Tension in a cable car's cable refers to the force exerted by the cable on the car. It is responsible for keeping the cable taut and supporting the weight of the car and its passengers.

2. How is tension in a cable car's cable calculated?

Tension in a cable car's cable can be calculated using the formula T = W + (2 * H * V^2)/g, where T is the tension, W is the weight of the car and its passengers, H is the height of the cable car above the ground, V is the speed of the cable car, and g is the acceleration due to gravity.

3. Why is tension important in a cable car's cable?

Tension is important in a cable car's cable because it determines the maximum weight that the cable car can safely carry and the maximum speed at which it can travel. It also ensures that the cable remains taut and does not sag, ensuring the safety and stability of the cable car.

4. How is tension controlled in a cable car's cable?

Tension in a cable car's cable is controlled by a tensioning system, which consists of a motor and a series of pulleys. The motor adjusts the tension in the cable by moving the pulleys, ensuring that the cable remains taut and the tension is within safe limits.

5. What happens if there is too much tension in a cable car's cable?

If there is too much tension in a cable car's cable, it can cause the cable to snap or the car to derail. This can result in serious accidents and injuries. Therefore, it is important to regularly check and maintain the tension in the cable car's cable to ensure the safety of passengers.

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