Answered

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At what angle should the roadway on a curve with a 50m radius be banked to allow cars to negotiate the curve at 12 m/s even if the roadway is frictionless?

Sagot :

onyebuchinnaji

Answer:

The road bank angle is 16.38⁰.

Explanation:

radius of curvature of the road, r = 50 m

allowable speed of car on the road, v = 12 m/s

The bank angle is calculated as;

[tex]\theta = tan^{-1} (\frac{v^2}{gr} )[/tex]

where;

θ is the road bank angle

g is acceleration due to gravity = 9.8 m/s²

[tex]\theta = tan^{-1} (\frac{v^2}{gr} )\\\\\theta = tan^{-1} (\frac{12^2}{9.8 \times 50} )\\\\\theta = tan^{-1} ( 0.2939)\\\\\theta = 16.38 ^0[/tex]

Therefore, the road bank angle is 16.38⁰.

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