Question

$\huge\bold{QUESTION}$
A cyclist speeding at 18km/h on a level road takes a sharp circular turn of radius 3m without reducing the speed and without bending towards the centre of the circular path. The coefficient of static friction between the tyres and the road is 0.1. Will the cyclist slip while taking the turn?

Answer 1

Given :

Speed of cyclist = 18km/hr

Radius of circular path = 3m

Coefficient of static friction = 0.1

To Find :

Cyclist takes circular turn without reducing the speed and without bending towards the centre, will the cyclist slip while taking the turn or not?

Solution :

❖ 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, v = √μrg

• v denotes max. safe velocity
• μ denotes coefficient of friction
• r denotes radius
• g denotes acc. due to gravity

By substituting the given values;

➙ v = √μrg

➙ v = √(0.1)(3)(10)

➙ v = √3

➙ v = 1.73 m/s

Here cyclist takes circular turn at a speed of 18km/h (5m/s) which is greater than maximum safe velocity$.$

∴ Cyclist will slip while taking the circular turn.

Answer 2

$\large\mathbb\colorbox{blue}{\color{white}{Refer\: Attachment}}$