Search
 
 

MATHEMATICS - CASE STUDY

    Introduction



Hanging Cable

 

An electric cable company is replacing the old cable in Dallas. Without the supporting steel cable, the electric cable that hangs between two poles form an arc because of the gravity. In the summer, the cable sinks for about 5 cm due to temperature, how much does the cable elongate?

What is known:

  • The distance between the two poles, L, is 10 meters.
  • The distance between the lowest point of the arc and the line of the top of the two poles, u, is 60 cm.
  • The mathematics formula to calculate the length of the cable, s, is
         
     
    Questions

 

 

How much does the cable elongate when its lowest point goes down for 5 cm?

     
    Approach


 
  • 1 meter equals 100 centimeters
  • The cable length,s, is a differentiable function. Differential du is independent variable and the differential ds is defined in terms of du by
    ds = f '(u)du.