The figure below shows the drive train of a bicycle that has wheels 67.3 cm in d

Question

The figure below 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 78.0 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter.

(a) Calculate the speed of a link of the chain relative to the bicycle frame.
m/s

(b) Calculate the angular speed of the bicycle wheels.
rad/s

(c) Calculate the speed of the bicycle relative to the road.
m/s

(d) What piece of data, if any, are not necessary for the calculations?

(a) Calculate the speed of a link of the chain relative to the bicycle frame. m/s (b) Calculate the angular speed of the bicycle wheels. rad/s (c) Calculate the speed of the bicycle relative to the road. m/s (d) What piece of data, if any, are not necessary for the calculations? diameter of front sprocket diameter of wheels angular rate length of pedal cranks diameter of rear sprocket none of these The figure below 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 78.0 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter.

Explanation / Answer

(a)according to the problem let us consider a tooth onthe front sprocket

   v = r
      = (0.152 m / 2) (78 rev / min) (2 rad / 1 rev) (1 min / 60 s)
      = 0.621 m / s
(b)consider the chain link engaging a tooth on the rearsprocket
   = v / r
       = 0.621 / (0.07 m / 2)
       = 17.74 rad / s
(c)now consider the wheel tread road
   a thread could be unwinding from the tire with thisspeed relative to the frame
   v = r
      = (0.673 / 2) *17.74
= 5.97m / s

D)length of pedal cranks

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