16. Figure P10.16 shows the drive train of a bicycle that has wheels 67.3 cm in

Question

16. Figure P10.16 shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter. Calculate (a) the 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?

Explanation / Answer

Given that the diameter of the wheel is dw = 67.3 cm = 0.673 m Diameter of the front sprocket is df = 17.5 cm = 0.175 m Diameter of the rare sprocket is dr = 7.00 cm = 0.07 m Angular velocity of the chain is = 76.0 rev/min                                                    = 7.954 rad/s   -------------------------------------------------------------------------------- (a) Linear speed of a link of the chain relative to the bicycle is                        v = (df / 2)                           = (0.175 m / 2) (7.954 rad/s)                             = 0.696 m/s (b) angular speed of the bicycle wheel is                     b = v / (dr /2)                           = 0.696m/s / (0.07m/2)                           = 19.89 rad/s (c) the speed of the bicycle relative to the road is                        v = (dw/2) b                           = (0.673 m / 2) (19.89 rad/s)                           = 6.692 m/s

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