Concept explainers
When a person pedals a bicycle, the front sprocket moves a chain that drives theback wheel and propels the bicycle forward. For each rotation of the frontsprocket, the chain moves a distance equal to the circumference of the frontsprocket. The back sprocket is smaller, so it will simultaneously move through agreater rotation. Furthermore, since the back sprocket is rigidly connected to theback wheel, each rotation of the back sprocket generates a rotation of the wheel.Suppose that the front sprocket of a bicycle has a 4-in. radius and the backsprocket has a 2-in. radius.
a. How muchchain will move with one rotation of the pedals (frontsprocket)?
b. How manytimes will the back sprocket turn with one rotation of thepedals?
c. How many times will the wheels turn with one rotation of the pedals?
d. If the wheels are 27 in. in diameter,how far wi11 the bicycle travel with one rotation of the pedals?
e. If the bicyclist pedals 80 rpm, what is the linear speed (in ft/min) of the bicycle?
f. If the bicyclist pedals 80 rpm, what is the linear speed (in mph) of the bicycle? (Hint:
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