a) What three physical quantities determine a minimum safe speed on a banked cur

Question

a) What three physical quantities determine a minimum safe speed on a banked curve of a racetrack? (Select all that apply.)
The coefficient of maximum static friction between the tires and the road surface.
The angle the road surface makes from the horizontal.
The weight of the vehicle.
The mass of the vehicle.
The coefficient of kinetic friction between the tires and the road surface.
The radii of the curves.

b)A racetrack is to have a banked curve with radius 240 m. What should be the angle of the bank if the normal force alone is to allow safe travel around the curve at 57.5 m/s?

Explanation / Answer

1)       With friction, for the minimum speed,               v = [rg(sin-scos)/(cos+ssin)]1/2       Wthout friction, for the minimum speed,               v = rgtan   ---> The coefficient of maximum static friction between the tires and the road surface.
  ---> The angle the road surface makes from the horizontal.
  ---> The radii of the curves. _______________________________________________________________________ _______________________________________________________________________ 2)       The radius of the banked curve, r = 240 m       The speed of the car, v = 57.5 m/s ________________________________________________________________________       Apply the Newton's second law of motion to the motion of the       car on banked curvem.       The y-component of the Newton's second law to solve for the normal force,                    The normal force, Fn= mg/cos                  The expression for the horizontal component of the       centripetal force Fc is                    Fc = Fnsin                         = [mg/cos]sin                         = mgtan              mv2/r = mgtan                   v2 = rgtan                   v2 = rgtan       Therefore, the angle of the banked curve is                    = tan-1[v2/rg]                       = tan-1[(57.5 m/s)2/(240 m)(9.8 m/s2)]                      = 54.57o                                     

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