The rear wheel of a multispeed bicycle is shown. The wheel has 32 spokes, with one-half...

The rear wheel of a multispeed bicycle is shown. The wheel has 32 spokes, with one-half being on either side (spokes on sides A and B are shown in the figur in black and red, respectively). For the tire to be properly centered on the frame of the bicycle, points A and B of the hub must be positioned at the same distance d from the centerline of the tire. To make room for the sprocket cluster, bicycle manufacturers give spokes on side B of the wheel a different orientation than spokes on side A. For the following questions, assume the tire is in the process of being manufactured, so that all spokes on side A have the same force F_A and all spokes on side B have the same force F_B.

(a) Determine the ratio of spoke forces F_B/F_A so that the resultant force in the x direction applied to the hub by all 32 spokes is zero. Hint: Although each spoke has a different orientation, all spokes on side A have the same length, and similarly all spokes on side B have the same length. Furthermore, all spokes on side A have the same x component of force, and all spokes on side B have the same x component of force.

(b) On which side of the wheel are the spokes most severely loaded?

(c) Briefl describe a new design in which spokes on both sides of the wheel are equally loaded and points A and B are at the same distance d from the centerline of the tire.