Assume a cyclist of weight mg can exert a force on the pedals equal to 0.90 mg on the average. If…

Assume a cyclist of weight mg can exert a
force on the pedals equal to 0.90 mg on the average. If the pedals rotate in a
circle of radius 18 cm, the wheels have a radius of 34 cm, and the front and
back sprockets on which the chain runs have 42 and 19 teeth respectively (Fig.
7-31), determine the maximum steepness of hill the cyclist can climb at
constant speed. Assume the mass of the bike is 12 kg and that of the rider is
65 kg. Ignore friction. Assume the cyclist’s average force is always: (a)
downward; (b) tangential to pedal motion.