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Figure P10.16 shows the drive train of a bicycle that has wheels $67.3 \mathrm{cm}$ in diameter and pedal cranks $17.5 \mathrm{cm}$ long. The cyclist pedals at a st...

Question

Figure P10.16 shows the drive train of a bicycle that has wheels $67.3 \mathrm{cm}$ in diameter and pedal cranks $17.5 \mathrm{cm}$ long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain engages with a front sprocket $15.2 \mathrm{cm}$ in diameter and a rear sprocket $7.00 \mathrm{cm}$ in diameter. Calculate (a) the (FIGURE CAN'T COPY) speed of a link of the chain relative to the bicycle frame, (b) the angular speed of the bicycle wheels, and (c) the speed of the bicycle re

Figure P10.16 shows the drive train of a bicycle that has wheels $67.3 \mathrm{cm}$ in diameter and pedal cranks $17.5 \mathrm{cm}$ long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain engages with a front sprocket $15.2 \mathrm{cm}$ in diameter and a rear sprocket $7.00 \mathrm{cm}$ in diameter. Calculate (a) the (FIGURE CAN'T COPY) speed of a link of the chain relative to the bicycle frame, (b) the angular speed of the bicycle wheels, and (c) the speed of the bicycle relative to the road. (d) What pieces of data, if any, are not necessary for the calculations?



Answers

SPEED OF A BICYCLE





The radii of the pedal sprocket, the wheel sprocket,
and the wheel of the bicycle in the figure are 4 inches,
2 inches,
and 14 inches, respectively. A cyclist is pedaling at a rate of 1 revolution per second.

(a)
Find the speed of the bicycle in feet per second and miles per hour.

(b)
Use your result from part (a) to write a function for the distance $d$ (in miles) a cyclist travels in terms of the number $n$ of revolutions of the pedal sprocket.

(c)
Write a function for the distance $d$ (in miles) a cyclist travels in terms of the time $t$ (in seconds). Compare this function with the $t$ function from part (b).

(d)
Classify the types of functions you found in parts(b) and (c). Explain your reasoning.


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