If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a problem on ice mountain roads).

(a) Calculate the ideal speed to take a 100.0 m radius curve banked at 15.0°.
(b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 20.0 km/h?

Explanation:

(a) radius of the curve, r = 100 m

Angle of banking,

The angle of banking is given by the formula as :

(b) Let is the minimum coefficient of friction. The force of friction is given by :

v = 20 km/h = 5.56 m/s

The first centripetal force is given by :

The second centripetal force is given by :

The additional friction force is given by :

Hence, this is the required solution.

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