Bicycles like the one shown in the photo in Figure P8.78 typically have 24 possible gear...

Bicycles like the one shown in the photo in Figure P8.78 typically have 24 possible gear ratios (three gears on the front and eight on the back). Suppose the diameters of the largest and smallest sprockets are 17 cm and 9.0 cm on the front cluster and 11 cm and 5.0 cm on the rear cluster. The inset drawing in Figure P8.78 gives an expanded view showing just one sprocket on the back and one on the front. The crank (Fig. P8.78, inset) measures 18 cm from the center of the pedal shaft axis to the center of the front sprocket, and the back wheel (including the tire) has a diameter of 68 cm. Assume the cyclist is traveling at constant speed. If a downward force of 320 N is applied to the pedal when the crank is in the horizontal position, what is the horizontal force the rear wheel exerts on the road for (a) the lowest and (b) the highest gear combinations? Also find the torque on the rear axle in both cases. Assuming rolling without slipping, how far does the bike move forward for each full pedal stroke (each full 360° rotation) for (c) the lowest and (d) the highest gear ratios?