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

In summary: So the net force on the pulley is: Ft-R(2000*9.81+2000*0.5)=ma Ft-(2000*9.81-2000*0.5)=ma The net force on the pulley is -2000 kg, or -500 newtons.
  • #1
marissa12
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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?


i know ALOT 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.
 

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  • #2
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?
 
  • #3
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.
 
  • #4
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).
 

1. What is tension?

Tension is a force that is exerted on an object, pulling it in opposite directions along its length. In the case of a cable car's cable, tension is the force that keeps the cable taut and supports the weight of the car and its passengers.

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

The tension in a cable car's cable is calculated using the formula T = (m x g) + (m x a), where T is the tension force, m is the mass of the car and its passengers, g is the acceleration due to gravity, and a is the acceleration of the car. This formula takes into account both the weight of the car and the additional force needed to accelerate it.

3. What factors affect the tension in a cable car's cable?

The tension in a cable car's cable is affected by several factors, including the weight of the car and its passengers, the acceleration of the car, the angle of the cable, and any external forces such as wind or friction. Changes in any of these factors can result in a change in tension.

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

Tension is important in a cable car's cable because it is what allows the cable to support the weight of the car and its passengers. If the tension is too low, the cable may sag and the car may not be able to move. If the tension is too high, the cable may become overstretched and could potentially break.

5. How is tension in a cable car's cable maintained?

Tension in a cable car's cable is maintained through a system of pulleys and counterweights. The pulleys help to evenly distribute the weight of the car along the cable, while the counterweights help to balance out any changes in the car's weight or acceleration. Regular maintenance and adjustments are also necessary to ensure that the cable remains taut and the tension is properly maintained.

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