Question

a cyclist speeding at 18 km/ h on a level road takes a sharp circular turn of radius 3 cm without reducing the speed , the co- efficient of static friction between the lyres and the road is 0.1 . will the cyclist slip while taking the turn?​

Answer 1

Answer :

Speed of cyclist = 18km/h

Radius of circular path = 3cm = 0.03m

Coefficient of friction = 0.1

We have to find whether the cyclist will slip or not while taking the turn$.$

★ A vehicle taking a circular turn on a level road. If μ is the coefficient of friction between tyres and road, then the maximum velocity with which the vehicle can safely take a circular turn at radius r is given by

• Vmax = √(μrg)

★ Conversion :

• 1 km/h = 5/18 m/s

∴ 18 km/h = 18 × 5/18 = 5 m/s

By substituting the given values, we get

➝ Vmax = √(μrg)

➝ Vmax = √(0.1 × 0.03 × 10)

➝ Vmax = √(0.03)

➝ Vmax = 0.17 m/s

ATQ, speed of cyclist is 5 m/s.

• V > Vmax

∴ Cyclist will slip while taking the turn.