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. Determine the force of friction exerted by the track on the tyres when the cycle is at B , C , and D . Take g = 10 m/s ^2 .

Step-by-step solution

Since the cycle moves with a constant speed, its tangential acceleration is zero ( a_t = 0 ). The net force along the tangential direction must be zero at all points on the track. The forces acting along the tangent are the tangential component of gravity and the force of friction. To maintain a constant speed, the friction force must exactly balance the tangential component of gravity. The magnitude of the friction force is given by f = mg , where is the angle made by the tangent to the track with the horizontal.