A motor cyclist wants to drive in horizontal circles on the vertical inner surface of a large cylindrical wooden well of radius $8.0 m$ , with minimum speed of $5 \sqrt{5} m s^{- 1}$ . The minimum value of coefficient of friction between the tyres and the wall of the well must be
$(g = 10 m s^{- 2})$

Question

A motor cyclist wants to drive in horizontal circles on the vertical inner surface of a large cylindrical wooden well of radius

8.0 m

, with minimum speed of

5 \sqrt{5} m s^{- 1}

. The minimum value of coefficient of friction between the tyres and the wall of the well must be

(g = 10 m s^{- 2})

Aicharya · Accepted Answer

The forces acting on the motor cyclist are, gravitational force $= m g$ , and frictional force $= μ N = μ \frac{m v^{2}}{r}$

By balancing forces, $\Rightarrow m g = μ \frac{m v^{2}}{r}$

$\Rightarrow \frac{g}{(\frac{v^{2}}{r})} = μ$

$\Rightarrow μ = \frac{10}{(\frac{{(5 \sqrt{5})}^{2}}{8})}$

$\Rightarrow μ = \frac{10 \times 8}{125}$

$\Rightarrow μ = 0.64$

A motor cyclist wants to drive in horizontal circles on the vertical inner surface of a large cylindrical…