The radii of the sprocket assemblies and the wheel of a bicycle are 4 inches, 2 inches, and 14 inches respectively. if the cyclist is pedaling at a rate of 1 revolution per second, find the speed of the bicycle in feet per second and miles per hour
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Ответ:
speed of bicycle =10 miles/h
Explanation:
given data
wheel radii front sprocket= 4 inches
wheel radii back sprocket = 2 inches
radii wheel = 14 inches
pedaling rate = 1 revolution per second
to find out
the speed of the bicycle in feet per second and miles per hour
solution
we know angular velocity ω is =
is angle and t is time
and linear velocity is V =
linear velocity is V = = rω
and
we know chain is attach top both sprockets
so velocity on front and back sprockets are equal
so rω front sprockets = rω back sprockets
4 inch × 1 rev/s = 2 inch × ω back sprockets
ω back sprockets = 2 rev/s
we can say here back sprockets is connect to back wheel
so
ω back sprockets = ω back wheel
so
velocity of bicycle = rω wheel
velocity of bicycle =14 inches × 2 rev/s
velocity of bicycle =14 inches × 2 (2 π ) rad/s
velocity of bicycle =56 π inches/s = miles / h
velocity of bicycle =10 miles/h
Ответ:
15 feet by 12 feet or 10 feet by 18 feet
Step-by-step explanation: