Explanation Calculation: Consider the given differential equation. d y d x = W T 1 Here, W is the vertical load. The per unit length of the roadbed is a constant ρ and the curve defining the cable is symmetric about x = 0 so only positive side of the bridge is to be conserved for the moment so, W = ρ x for 0 ≤ x ≤ L 2 The equation can be written as, d y d x = ρ x T 1 Separate the variable of the above equation. d y = ρ x T 1 d x Integrate on both sides of the equation. ∫ d y = ∫ ρ x T 1 d x y = ρ 2 T 1 x 2 + c Substitute a for y and 0 for x in the above equation. a = ρ 2 T 1 ( 0 ) 2 + c a = c Substitute a for c in above equation. y = ρ 2 T 1 x 2 + a The maximum height of ( a + h ) happens at the end of the bridge, x = L 2

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 2.2, Problem 53E

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Chapter 2 Solutions

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