MATH 106 Lecture Notes - Lecture 3: Tangent

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Use the following form for the catenary curve:  

Where T is the tension on the line, w is the unit weight of the line, x is zero at the lowest point of
the hanging transmission line and k deals with the height of the low point above the ground.
The two power poles we are dealing with are 600 feet apart and each pole is 150 feet tall. The
attachment point for the lowest line is 80 feet above the ground (three other lines are placed above this
lowest line). Place your coordinate system with its origin at the midpoint between the two poles and on
the ground.
1. A.) If the tension on the transmission line is 5000 pounds and the unit weight of the line is 1.5
pounds per foot. Find the equation for this catenary curve.
 

  
 

 
 

 
  
  
  
 

First, the original equation was taken and because we know that T=Tension w=unit of weight on the
line 5ft gets plugged in for all the T’s and .5lb/ft gets plugged into all the w’s. We also know
that when x=300 then y=80 so those get plugged in as well. On the right side everything that can get
multiplied does then gets subtracted from the left and right side. The right side cancels out and gives
us a value of -3266.842448ft for K. Now that k is found it just gets plugged in for K which resulted in
our equation because that was the only unknown variable.
B.)What is the height of the lowest point of this transmission line?
  
 

  
 

  
 
  
  ft
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Document Summary

Use the following form for the catenary curve: (cid:1877)=(cid:3050)cosh(cid:4672)(cid:3050)(cid:1876)(cid:4673)+ The two power poles we are dealing with are 600 feet apart and each pole is 150 feet tall. The attachment point for the lowest line is 80 feet above the ground (three other lines are placed above this lowest line). Place your coordinate system with its origin at the midpoint between the two poles and on the ground: a. ) If the tension on the transmission line is 5000 pounds and the unit weight of the line is 1. 5 pounds per foot. Find the equation for this catenary curve. (cid:1877)=(cid:1875)cosh(cid:4672)(cid:1875)(cid:1876)(cid:4673)+ (cid:1877)=(cid:887)(cid:882)(cid:882)(cid:882)(cid:883). (cid:887) cosh((cid:883). (cid:887)(cid:887)(cid:882)(cid:882)(cid:882)(cid:1876))+ (cid:890)(cid:882)=(cid:887)(cid:882)(cid:882)(cid:882)(cid:883). (cid:887) cosh((cid:883). (cid:887)(cid:887)(cid:882)(cid:882)(cid:882) (cid:885)(cid:882)(cid:882))+ (cid:890)(cid:882)=(cid:885)(cid:885)(cid:886)(cid:888). (cid:890)(cid:886)(cid:884)(cid:886)(cid:886)(cid:890)+ (cid:890)(cid:882) (cid:885)(cid:885)(cid:886)(cid:888). (cid:890)(cid:886)(cid:884)(cid:886)(cid:886)(cid:890)= (cid:885)(cid:884)(cid:888)(cid:888). (cid:890)(cid:886)(cid:884)(cid:886)(cid:886)(cid:890)= (cid:1877)=(cid:887)(cid:882)(cid:882)(cid:882)(cid:883). (cid:887) cosh((cid:883). (cid:887)(cid:887)(cid:882)(cid:882)(cid:882)(cid:1876)) (cid:885)(cid:884)(cid:888)(cid:888). (cid:890)(cid:886)(cid:884)(cid:886)(cid:886)(cid:890) (cid:1877)=(cid:887)(cid:882)(cid:882)(cid:882)(cid:883). (cid:887) cosh((cid:883). (cid:887)(cid:887)(cid:882)(cid:882)(cid:882)(cid:1876)) (cid:885)(cid:884)(cid:888)(cid:888). (cid:890)(cid:886)(cid:884)(cid:886)(cid:886)(cid:890) (cid:1877)=(cid:887)(cid:882)(cid:882)(cid:882)(cid:883). (cid:887) cosh((cid:883). (cid:887)(cid:887)(cid:882)(cid:882)(cid:882)(cid:4666)(cid:882)(cid:4667)) (cid:885)(cid:884)(cid:888)(cid:888). (cid:890)(cid:886)(cid:884)(cid:886)(cid:886)(cid:890) (cid:1877)=((cid:887)(cid:882)(cid:882)(cid:882)(cid:883). (cid:887) (cid:883)) (cid:885)(cid:884)(cid:888)(cid:888). (cid:890)(cid:886)(cid:884)(cid:886)(cid:886)(cid:890) (cid:1877)=(cid:885)(cid:885)(cid:885)(cid:885). (cid:885)(cid:885)(cid:885)(cid:885)(cid:885)(cid:885) (cid:885)(cid:884)(cid:888)(cid:888). (cid:890)(cid:886)(cid:884)(cid:886)(cid:886)(cid:890) (cid:1877)=(cid:888)(cid:888). (cid:886)(cid:891)(cid:882)(cid:891)ft.

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