A car rounds a 50 meter radius curve that is banked such that a car rounding it

Question

A car rounds a 50 meter radius curve that is banked such that a car rounding it does not need friction at a speed of 12 m/s. What is the bank angle of the road?

The coefficient of kinetic friction between the tires and the road is 0.5 and the coefficient of static friction between the tires and the road is 0.8. If the same road were flat (instead of banked), determine the maximum speed with which the coar could round the curve.

Back to the banked curve- if the coefficient of static friction between the tires and the road is 0.8, what is the maximum speed with which this car can round the curve?

Thank you!!!!

Explanation / Answer

1)

Fnet = Fcentripetal

mgtan(theta) = mv^2/r

v^2 = r*g*tan(theta)

tan(theta) = v^2 / r*g)

theta = tan^-1(v^2 / r*g)

theta = tan^-1(12^2 / 50*9.81)

theta = 16.36 degree.

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