On an icy winter day, the coefficient of friction between the tires of a car and a roadway is reduced to 3/5 its value on a dry day. As a result, the maximum speed vmax dry at which the car can safely negotiate a curve of radius R is reduced. The new value for this speed is what percentage of its value on a dry day?

Question

anonymous · Answer

When a car moves along the circular curve it is found under the action of the centrifugal force(which is pseudo force, but it doesn't matter here)
$$F_{centrifugal}=\frac{mv^2}{r}$$
The car will move without sliding as long as friction is there. So by N's third law
$$F_{friction} = F_{centrifugal}$$
$$F_{friction} = mg\mu$$
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So the velocity at which the car can safely negotiate a curve of radius R is
$$v=\sqrt(\mu gr)$$