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The cable cars in San Francisco are pulled along their
Chapter 7, Problem 16E(choose chapter or problem)
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 Figure EX7.16. 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?
Equation Transcription:
Text Transcription:
100 ft
1.5 m
Questions & Answers
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 Figure EX7.16. 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?
Equation Transcription:
Text Transcription:
100 ft
1.5 m
ANSWER:Step 1 of 2
We have to find the tension in the cable car's cable.
The Tension (Force) in the block can be found using Newton's second law.
\(T=m g\)
Where,
\(m=\) mass of block \(=2,00 \mathrm{~kg}\)
\(g=\) acceleration of the gravity
\(=9.80 \mathrm{~m} / \mathrm{s}^{2}\)
Thus,
\(T=2,000 \times 9.80\)
\(=19,600 \mathrm{~N}\)