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?
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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.
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