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A road with a radius of 75.0 m is banked so that a car can navigate...

A road with a radius of 75.0 m is banked so that a car can navigate the curve at a speed of 15.0 m/s without any friction. If the banking angle is reduced to zero when a car is going 20.0 m/s on this curve, what minimum coefficient of static friction is needed if the car is to navigate the curve without slipping?

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Answer #1

Since the banking angle is reduced to zero, frictional force (static friction) alone is to provide the centripetal force to prevent car from slipping.

Given radius of road R = 75.0 m

Velocity of the car v = 20 m/s

The condition for not to slip is

Here, is the coefficient of static friction

and g is acceleration due to gravity.

The above equation is rearranged as

Hence, the minimum value of coefficient of static friction is given by the expression

Therefore, the minimum value of coefficient of static friction is 0.5442

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