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

[marissa12]

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?


i know a lot of the info is unecessary..
but wouldn't you need to know the mass of the cable car? because i think that the tensioning pulley.. just shows that it is in equlibrium so you don't need it.

 

[Doc Al]

Consider the horizontal forces acting on the "tensioning pulley". Since it's in equilibrium, what must be the net force on it? Thus what must be the tension in the cables? Hint: What's the tension in the cable attached to the hanging block?

 

[marissa12]

is the Ft in the cable attached to the block:

Ft-fg(2000*9.81)=ma Ft-(2000*9.81)=(2000)(a)

if its in equilib. then the net force is zero.

 

[Doc Al]

Yes, the pulley and the block are both in equilibrium, so the net force on each is zero.

What are the forces on the pulley? You have the rope tension pulling to the left. (What is that tension? You didn't finish the calculation that you started, but you were on the right track.) And you have the tension in the cables pulling to the right. Note that the cable has two sections pulling on the pulley (that's the big hint).