Question

5. A highway curve with radius 900 ft is banked so that a car traveling at 55 mph will not skid sideways even in the absence of friction. At what angle should the curve be banked to prevent skidding?

14.6°
10.9°
18.9°
12.7"

Answer 1

Answer: The angle at the curve should be banked to prevent skidding by 12.68⁰.

Step-by-step explanation:

At a banked road curve

Horizontal factor = mgsinθ

And the factor of centrifugal force = mv²/r*cosθ

In absence of friction, a car can travel without skid if:

mv^2/r*cosθ = mgsinθ or tanθ = mv²/(g*r)

Given, radius of curve, r = 900ft = 900*0.305 = 274.5m

v = 55 mph = 55*0.447 = 24.585 m/s

and g = 9.81 m/s^2

So, tanθ = (24.585)²/(9.8*274.5) = 0.225

θ = 12.68⁰

Therefore, The angle at the curve should be banked to prevent skidding by 12.68⁰.