A car is travelling at $57.6 ext{ km/hr}$ on an unbanked (horizontal) circular road of radius $160

Question

A car is travelling at $57.6 	ext{ km/hr}$ on an unbanked (horizontal) circular road of radius $160/3 	ext{ m}$. If the coefficient of friction between the road and the car is $0.8$, then the maximum tangential deceleration that driver of car can achieve by applying the brakes at this moment is : ($g = 10 	ext{ m/s}^2$)

Professor PC Thomas Classes · Answer

Velocity $v = 57.6 	ext{ km/hr} = 57.6 	imes (5/18) 	ext{ m/s} = 16 	ext{ m/s}$. Centripetal acceleration $a_c = v^2/r = 16^2 / (160/3) = 256 	imes 3 / 160 = 4.8 	ext{ m/s}^2$. Maximum possible total acceleration is provided by limiting friction, $a_{max} = \mu g = 0.8 	imes 10 = 8 	ext{ m/s}^2$. Total acceleration is $a = \sqrt{a_t^2 + a_c^2}$, where $a_t$ is tangential deceleration. Thus $a_t = \sqrt{a_{max}^2 - a_c^2} = \sqrt{8^2 - 4.8^2} = \sqrt{64 - 23.04} = \sqrt{40.96} = 6.4 	ext{ m/s}^2$.