A track consists of two circular parts ABC and CDE of equal radius 100 m , joined smoothly. Each part subtends a right angle at its centre. A cycle weighing 100 kg together with the rider travels at a constant speed of 18 km/h on the track. What should be the minimum friction coefficient between the road and the tyre to ensure that the cyclist can move with constant speed? Take g = 10 m/s ^2 .

Step-by-step solution

The track is in a vertical plane. For the two circular arcs to join smoothly and each subtend 90^ at their respective centers, the track must have horizontal tangents at the lowest point of the concave part (valley) and the highest point of the convex part (hill). The angle made by the radius with the vertical varies from 0^ to 45^ for both parts. For the cyclist to move at a constant speed v , the net tangential force must be zero. Thus, the required friction force balances the tangential component of gravity: f =