The figure below shows the drive train of a bicycle that has wheels67.3 cm in di

Question

The figure below shows the drive train of a bicycle that has wheels67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclistpedals at a steady angular rate of75.0 rev/min. The chain engages with a frontsprocket 15.2 cm in diameter and a rear sprocket 6.20 cm in diameter.

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

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

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

(d) What pieces of data, if any, are not necessary for thecalculations? (Select all that apply.)

Explanation / Answer

(a)
   according to the problem let us consider a tooth onthe front sprocket
   v = r
      = (0.152 m / 2) (75 rev / min) (2 rad / 1 rev) (1 min / 60 s)
      = ....... m / s
(b)
   consider the chain link engaging a tooth on the rearsprocket
   = v / r
       = v / (0.062 m / 2)
       = ..... 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) ()
= ...... m / s
(d)

   we did not need to know the length of the pedalcranks

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