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?

• A. 7 m/s
• B. 11 m/s
• C. 14 m/s
• D. 16 m/s

Answer 1

The correct option is B 11 m/s

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)

F_net = F_centripital

mg tanθ = mv²/r

v² = rg tanθ

$v=\sqrt{rgtan\theta }$

= $\sqrt{\left(50m\right)\left(9.8m/s^2\right)\left(tan{15}^{\circ }\right)}$ = 11 m/s

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