Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_98

7/98 The figure shows the side view of the wheel carriage (truck) of a railway passenger car where the vertical load is transmitted to the frame in which the journal wheel bearings are located. The lower view shows only one pair of wheels and their axle, which rotates with the wheels. Each of the 33-in.-diameter wheels weighs 560 lb, and the axle weighs 300 lb with a diameter of 5 in. Both wheels and axle are made of steel with a specific weight of 489 lb/ft³. If the train is traveling at 80 mi/hr while rounding an 8° curve to the right (radius of curvature 717 ft), calculate the change \(\Delta R\) in the vertical force supported by each wheel due only to the gyroscopic action. As a close approximation, treat each wheel as a uniform circular disk and the axle as a uniform solid cylinder. Also assume that both rails are in the same horizontal plane.