Question

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola
The roadway which is horizontal and 100 m long is supported by vertical
attached to the cable, the longest wire being 30 m and the shortest being 6m.
Find the length of a supporting wire attached to the roadway 18 m from the middle.​

Answer 1

Answer:

The length of the supporting wire is 9.11 m .

Step-by-step explanation:

The roadway is 100 m long horizontally.

Uniform suspension bridge, the cable hangs in the form of a parabola .

Thus, the equation of the parabola becomes= x^2 = 4ay

The cable is symmetrical along the axis with 50m length on each side.

The longest and shortest vertical supporting wires are 30m and 6m respectively.

If these wires are connected from opposite sides, the vertical extent of the suspension becomes 24 m.

Substituting these values , as they lie on the parabola :

=50 * 50 = 4 a * 24

> a = 2500/96

Now we need to find the length of a supporting wire attached 18m from the middle.

Let this length of the wire be x meters.

So, the point , 18 and x - 6 lies on the parabola

=18 * 18 = 4 * a * ( x - 6 )^2

> 18 * 18 = 4 * 2500/96 * (x - 6)^2

Solving we get x = 9.11 m .