Question

An unbanked (flat) curve of radius 150 m is rated for a maximum speed of 32.5 m/s. At what maximum speed, in m/s, should a flat curve with radius of 65.0 m be rated

Answer 1

The maximum speed is 21.39 m/s.

Step-by-step explanation:

Given;

radius of the flat curve, r₁ = 150 m

maximum speed,
`v_(max)` = 32.5 m/s

The maximum acceleration on the unbanked curve is calculated as;

`a_c_(max) = (V_(max)^2)/(r) \\\\a_c_(max) = (32.5^2)/(150) \\\\a_c_(max) = 7.04 \ m/s^2`

the radius of the second flat curve, r₂ = 65.0 m

the maximum speed this unbanked curve should be rated is calculated as;

`a_c_(max) = (V_(max)^2)/(r_2) \\\\V_(max)^2 = a_c_(max) \ * \ r_2\\\\V_(max) = \sqrt{a_c_(max) \ * \ r_2} \\\\V_(max) =√(7.04 \ * \ 65) \\\\V_(max) = 21.39 \ m/s`

Therefore, the maximum speed is 21.39 m/s.