College Physics with MasteringPhysics 7th Edition by Jerry Wilson,Anthony Buffa,Bo Lou

Exercise 38

The forces acting on Einstein and the bicycle (Fig. 2 of the Insight 8.1, Stability in Action) are the total weight of Einstein and the bicycle ( mg ) at the center of gravity of the system, the normal force ( N ) exerted by the road, and the force of static friction ( f s ) acting on the tires due to the road. (a) If Einstein is to maintain balance, should the tangent of the lean angle (tan ) be (1) greater than, (2) equal to, or (3) less than f s / N (b) The angle in the picture is about 11°. What is the minimum coefficient of static friction µ s between the road and the tires (c) If the radius of the circle is 6.5 m, what is the maximum speed of Einstein's bicycle [ Hint : The net torque about the center of gravity must be zero for rotational equilibrium.]