Two friends are planning to go on RAGBRAI (Register’s Annual Great Bike Ride Across Iowa) next year. One is planning to ride a mountain bicycle with 26 in. tires, and the other has a touring bicycle with 27 in. tires. A typical RAGBRAI is about 480 mi long.
(a) How many more revolutions will the mountain bike tires make in that distance than the touring bike?
(b) Typical gearing for most bicycles ranges from 30 to 50 teeth on the chain wheel (front gears) and 12 to 30 teeth on the rear cog. Find how many more revolutions of the pedals the mountain biker will make during the trip, using an average pedaling time of 85 percent of the trip and a 42-tooth chain wheel and a 21-tooth rear cog for your calculations.
(c) If both cyclists have 170 mm cranks on their bikes, what will be the mechanical advantage (considering only the movement of the feet with a constant force for walking and riding), in percent, that each rider will have achieved over walking the same distance? (This can be found by dividing the distance walked by the distance the feet move in riding.)
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