The Daytona 500 stock car race is held on a track that is ap

The Daytona 500 stock car race is held on a track that is approximately 2.5 mi long, and the turns are banked at an angle of 31°. It ls currently possible for cars to travel through the turns at a speed of about 168 mi/h. Assuming these cars are on the verge of slipping into the outer wall of the racetrack, find the coefficient of static friction between the tires and the track. (Assume that the track is circular.) Need Help?Read It Talk to a Tutor

Solution

from the given data

Radius of the track, R = 2.5*1609/(2*pi) m

= 640 m

Vmax = 168 mi/h

= 168*1.609*5/18 m/s

= 75.1 m/s

theta = 31 degrees

we know,

maximum speed with which a vehicle can take turn safely on banked curved path,

Vmax = sqrt(R*g*(mue_s + tan(theta)/(1 - mue_s*tan(theta) )

Vmax^2 = R*g*(mue_s + tan(theta)/(1 - mue_s*tan(theta)

75.8^2 = 640*9.8(mue_s + tan(31))/(1 - mue_s*tan(31)

==> mue_s = 0.203 <<<<<<----------------Answer