A cyclist speeding at 18 km/h on a level road takes a sharp circular turn of radius 3 m without redu

Question

A cyclist speeding at 18 km/h on a level road takes a sharp circular turn of radius 3 m without reducing the speed. The co-efficient of static friction between the tyres and the road is 0.1. Will the cyclist slip? (Take g = 9.8 m/s²)

Professor PC Thomas Classes · Answer

Speed is $v = 18$ km/h $= 5$ m/s. The maximum safe speed is $v_{max} = \sqrt{\mu_s R g} = \sqrt{0.1 	imes 3 	imes 9.8} = \sqrt{2.94} \approx 1.71$ m/s. Since 5 m/s > 1.71 m/s, the cyclist will slip.