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?

Please answer all of them :3, thanks!!!

Answer 1

when the road is banked :

r = radius of the curve = 50 m

v = speed of car = 12 m/s

= angle of banking = ?

Using the equation

tan = v²/(rg)

tan = (12)² /(50 x 9.8)

tan = 0.294

= 16.4 deg

when the road is flat :

= Coefficient of static friction = 0.8

r = radius = 50 m

V_max = maximum speed of car = ?

using the equation

V²_max = rg

V²_max = (0.8) (50) (9.8)

V_max = 19.8 m/s

= coefficient of static friction = 0.8

= banking angle = 16.4 deg

r = radius of curve = 50 m

maximum speed is then given as

v = sqrt(rg(tan + )/(1 - tan))

v = sqrt(50 x 9.8 (tan16.4 + 0.8)/(1 - (0.8) tan16.4))

v = 26.5 m/s