Chapter 10, Problem 101GP

When bicycle and motorcycle riders “pop a wheelie,” a large acceleration causes the bike’s front wheel to leave the ground. Let M be the total mass of the bike-plus-rider system: let x and y be the horizontal and vertical distance of this system’s CM from the rear wheel’s point of contact with the ground (Fig. 10–72). (a) Determine the horizontal acceleration a required to barely lift the hike’s front wheel off of the ground, (b) To minimize the acceleration necessary to pop a wheelie, should x be made as small or as large as possible? How about y? How should a rider position his or her body on the bike in order to achieve these optimal values for x and y? (c) If x = 35 cm and y = 95 cm, find a.