Question 526688: The pedal sprocket has a radius of 4 in., the wheel sprocket has a radius of 2 in., and the wheel a radius of 13 in. The cyclist pedals at 38 rpm.
(a) Find the rotations per minute of the wheel sprocket.
(b) Find the speed of the bicycle. Assume that the wheel turns at the same rate as the wheel sprocket.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! The pedal sprocket has a radius of 4 in., the wheel sprocket has a radius of 2 in., and the wheel a radius of 13 in. The cyclist pedals at 38 rpm.
(a) Find the rotations per minute of the wheel sprocket.
(b) Find the speed of the bicycle. Assume that the wheel turns at the same rate as the wheel sprocket.
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(a) Since the radius of the pedal sprocket is twice that of the wheel sprocket, it has twice the circumference(2πr) of the wheel sprocket, that is, every time the pedal makes one revolution the wheel makes two revolutions. So the wheel sprocket turns at 2*38=76 rpm.
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(b) Circumference of the 13 in wheel=2π*13=26π in.
For each revolution the wheel travels 26π in
The speed of the bicycle=26π in/rev*76 rev/min=26π*76 in/min
=1976π in/min*ft/12in*mile/5280ft*60min/hr
=1976π*60/12*5280 mph
≈5.88 mph
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