The cable cars in San Francisco are pulled along their tracks by an underground

Question

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 m = 2200 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?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

The cable car is moving with constat speed, so the acceleration of the car is zero and hence net force acting on the system is zero.

The force acting on the car are cable along the pulley and steel cable suspended with mass.

The tension in all the cable should be equal, since the system is in equlibrium.

The tension in the steel cable is T = mg, thus the net force in system is,

     2T = mg

Therefore, the tension in the cable is T = mg/2 = (2200 kg)(9.8m/s^2)/2 = 10780 N

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