Question

A curve has a radius of 50 meters and a banking angle of 15º. What is the ideal, or critical, speed (the speed for which no friction is required between the car's tires and the surface) for a car on this curve?

Answer 1

Explanation:

Here, radius of curve, r = 50 m

banking angle, θ = 15º

free-fall acceleration, g = 9.8 m/s2

We have to find out the ideal speed v (the speed for which no friction is required between the car's tires and the surface)

From the free-body diagram for the car:-

Fnet = Fcentripital

mg tanθ = mv^2/r

v2 = rg tanθ

v = √rg tanθ

 = √(50 m) (9.8 m/s2) (tan 15º) = 11 m/s

If the car has a speed of about 11 m/s, it can negotiate the curve without any friction.