Calculating Tension Force: Cable Cars in San Francisco

[Xaspire88]

Question:
The cable cars in San Francisco are pulled along their tracks by an underground steel cable that moves along at 9.5mph. 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 the cable stretches by up to 100ft 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 diagram <http://img245.imageshack.us/img245/1350/cablecarib9.jpg>. A 2000kg block is attached to the tensioning pulley's cart, via a rope and pulley, and is suspended in a deep hole. Q:What is the tension in the cable car's cable

My question is:
1. Since the cable is not accelerating can it be treated as if it is just fixed?
2. Is the 9.5 mph, 100ft stretching and the diameter of the pulley relevant information. It seems to me that most of that is not necessary to solving this problem.

When i first attempted to solve this it seemed that the tension force that the cable would be feeling would be equal in magnitude to the force applied to the cable car by the 2000kg block. Is this reasoning correct?

 

[Xaspire88]

Any help would be very appreciated :)

Edit:(had a thought)

Would the tension that the cable car's cable would feel be half that of the total force being applied to the cable car since it is being essentially between two cables?

 

[Moetasim]

I would approach this problem by first understanding the physics principles involved. The cable car system in San Francisco operates on the principle of tension, where the cable is pulled along by the force of the motor and the tension in the cable keeps it taut. The tension force is the force that is transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends. In this case, the tension force is what keeps the cable car moving along its tracks.

To calculate the tension in the cable car's cable, we need to consider the forces acting on the cable car system. The 2000kg block attached to the tensioning pulley's cart is suspended in a deep hole, which means it is not moving and therefore not contributing to the movement of the system. The only relevant forces are the force applied by the cable car motor and the force applied by the tensioning pulley. These forces must be equal in magnitude in order to keep the cable taut and the cable car moving at a constant speed.

The 9.5 mph speed of the cable is not relevant to calculating the tension force, but the 100ft stretching of the cable is important. This stretching must be accounted for when calculating the tension force as it will affect the overall length and tension of the cable. The diameter of the pulley is also relevant as it determines the amount of force applied by the pulley on the cable.

To answer the first question, the cable can be treated as fixed as long as it is not accelerating. In this case, the cable car is moving at a constant speed, so we can treat the cable as fixed.

To calculate the tension force, we can use the formula T = m*a, where T is the tension force, m is the mass of the cable car, and a is the acceleration of the cable car. Since the cable car is moving at a constant speed, the acceleration is 0 and therefore the tension force is also 0.

In conclusion, the tension force in the cable car's cable is 0, as the cable car is moving at a constant speed and there are no external forces acting on the system. The 2000kg block suspended in the deep hole does not contribute to the movement of the system and therefore does not affect the tension force. The relevant factors to consider when calculating the tension force are the force applied by the motor, the force applied by the tensioning pulley