A racing car travels on a track (without banking) ABCDEFA. ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The coefficient of friction on the road is `mu = 0.1`. The maximum speed of the car is `50 ms^(-1)`. Find the minimum time for completing one round.

Explanation

Frictional force provide necessary centripetal force in uniform circular motion
for AOC path radius = 2R
Centripetal force `(mv^(2))/(r ) =f`
` f= mu N`
`v = sqrt( mu r g)`
for path ABC
path length `= (3)/(4) (2pi xx 2R) = 3piR = 3 pi xx 10 =300 pi m`
`t_(1) = (300pi)/(14.14) = 66.6 s`
for path DEF
path length `=(1)/(2) (2pi R ) = (pi xx 100)/( 2 ) =50 pi`
` t_(2) = (50pi)/( 10) = 5pi s = 15.7 s`
For path CD and FA
path length R=R = 2R =200 M
`t_(3) = (200)/( 50) = 4.0s`
Total time for completing one round `t= t_(1) + t_(2) + t_(3) = 66.6 + 15.7 + 4.0 = 86.3 s`