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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
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B
11 m/s
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C
14 m/s
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D
16 m/s
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Solution

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)

Fnet = Fcentripital

mg tanθ = mv2/r

v2 = rg tanθ

v=rgtanθ

= (50m)(9.8m/s2)(tan 15) = 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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