Question

What is the minimum radius of a circle along which a cyclist can ride with a velocity 18 km/hr if the coefficient of friction between the tyres and the road is  = 0.5

Answer 1

Answer: The radius is 5m

Explanation:18km/hr =5m/s

we know,

               V =  √urg

              5 = √0.5×r×9.8

               squaring on both sides,

            25 = r×4.9

           ∴r is approximately 5m

Answer 2

Answer:

The minimal radius of the circle alongside which the bicycle owner can journey with a pace of 18 km/hr (or 5 m/s) and a coefficient of friction of 0.5 is about 13.88 meters.

Explanation:

From the above question,

The minimal radius of a circle alongside which a bicycle owner can journey with a pace of 18 km/hr, we want to use the equation for centripetal force:

                            F = m$v^2$ / r

where F is the centripetal force, m is the mass of the bike owner and the bicycle, v is the speed of the cyclist, and r is the radius of the circle.

The most frictional pressure that can act on the bicycle owner and the bicycle is given by:

                           f = μN

where f is the most frictional force, μ is the coefficient of friction between the tyres and the road, and N is the everyday pressure appearing on the bicycle owner and the bicycle.

Since the centripetal pressure required to journey in a circle is supplied by way of friction, we can equate these two forces and resolve for the radius:

                            F = f

                            m$v^2$ / r = μN

Substituting N = mg (where g is the acceleration due to gravity), we get:

                            m$v^2$ / r = μmg

Solving for r, we get:

                             r = m$v^2$ / (μmg)

Substituting the given values, we get:

                             r = (3.6 m/s)$.^{2}$ / (0.5 x 9.8 m/$s^{2}$)

                             r = 13.88 meters

Therefore,

        The minimal radius of the circle alongside which the bicycle owner can journey with a pace of 18 km/hr (or 5 m/s) and a coefficient of friction of 0.5 is about 13.88 meters.

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