A designer plans to build a circular Indy 500 racetrack with a bank angle of 12o and it must keep cars moving at 150 miles per hour (242 km per hour) from sliding off the track even when the track is slick.
a) Draw a diagram showing all forces acting on a racecar as it rounds the track. Neglect friction.
b) Choose an x-y coordinate system and write the components of the forces. Why is the choice of a horizontal x-axis going to be better than the choice of an x-axis parallel to the track surface?
c) What conditions do you impose on the x acceleration to make this a circular motion problem?
d) What condition do you impose on the y acceleration so the car does not slide up or down the bank of the track?
e) Use the equations for x and y in part b) to show that tan θ = v2/(g r), is the condition for going around the circular track without sliding up or down the track in the absence of friction where v is the speed of the race car, r is the radius of the track, and θ is the bank angle.
f) What is the proper radius of the Indy 500 track in this problem for the bank angle of 12 degrees?
g) How long does it take a racecar to complete a lap around this track at a constant 242 km/hr?