Question

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 is currently possible for cars to travel through the turns at a speed of about 164 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.)

Answer 1

Solution:-From the question we have

=r = C/2PI = 4022.5/6.28 = 640.5 m

V = 164 mph = 164*1.606/3.6 = 73.16 m/sec
ac = V^2/r = 73.16^2/640.5 = 8.36 m/sec^2

N cosθ = mg >>>> N = mg / cosθ
fs = μ N = μ (mg/cosθ) = μmg/cosθ


ΣF = mv2 / R

=> N sinθ + fs cosθ = mv^2 / R

=>(mg/cosθ)(sinθ) + (μmg/cosθ)(cosθ) = mv^2 / R

=>mg(tanθ) + mgμ = mv^2 / R

=> tanθ + μ = (v^2) / (R*g)

putting the values:-

tan(31)+μ= (73.16)^2/( 640.5*9.8)

=> μ= [(73.16)^2/( 640.5*9.8)]-tan(31)

= 0.252