Question

An electrical cable is to be suspended in this system. The machines are in a distance L=4.56 meters apart. The cable forms the shape of a catenary of the form = ℎ (/) where – L/2 ≤ x ≤ L/2. Determine the fixing point height (y) if the minimum clearance (c) is to be 5m at the centre line of the catenary.

Answer 1

The fixing point height of the electrical cable that forms a catenary curve between two poles is 5 meters to ensure the minimum clearance of 5 meters at the center of the span.

Step-by-step explanation:

The question involves determining the fixing point height of an electrical cable that forms a catenary curve between two poles. The formula of the catenary curve is given as y = h cosh(x/a), where L is the horizontal distance between the poles. We are given that the minimum clearance at the center, which is the lowest point of the catenary, should be 5 meters. This clearance occurs at x = 0, since the center of the catenary is the midpoint between the poles. By setting the given constraint that y must be at least 5 meters at x = 0 and knowing that the distance between the poles L is 4.56 meters, we can find the height h of the fixing points at the poles.

To solve this, we use the equation at the center of the catenary, substituting x = 0 to find h. This gives us:

5 = h cosh(0/a)

Since cosh(0) = 1:

5 = h

Therefore, the fixing point height of the cable must be 5 meters to ensure the minimum clearance of 5 meters at the lowest point of the catenary.