Finding the tension in the cable

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SUMMARY

The discussion focuses on calculating the tension in a steel cable used for a ski gondola, which is 580 meters long with a diameter of 1.5 cm. The speed of a wave pulse traveling along the cable was determined to be 61.05 m/s after a round trip time of 19 seconds. To find the tension in the cable, one must relate the speed of the wave to the tension and the linear mass density of the cable, which requires knowledge of the density of steel.

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  • Understanding of wave mechanics and speed calculations
  • Knowledge of linear mass density and its calculation
  • Familiarity with the properties of steel, specifically its density
  • Basic physics concepts related to tension and forces
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  • Research how to calculate linear mass density of materials, specifically steel
  • Learn about the relationship between wave speed, tension, and linear mass density in cables
  • Study the principles of wave propagation in solid materials
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Students in physics or engineering, particularly those studying mechanics and material properties, as well as professionals involved in cable design and analysis.

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Homework Statement


A ski gondola is connected to the top of a hill by a steel cable of length 580 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 19 s for the pulse to travel the length of the cable and then return.

(a) What is the speed of the pulse?
61.05263158 m/s
(b) What is the tension in the cable?
? N


Homework Equations


I would assume you would sum the forces, but I don't know what to put together to reach a tension.


The Attempt at a Solution


I do not know where to begin.

Help is greatly appreciated! Thank you!
 
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How is the speed related to the tension and the linear mass density? You will have to look up the density of steel to figure out the linear mass density of this cable.
 

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