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 79.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter. Calculate the speed of a link of the chain relative to the bicycle frame. m/s Calculate the angular speed of the tricycle wheels. rad/s Calculate the speed of the bicycle relative to the road. m/s what piece of data, if any, are not necessary for the calculations? Diameter of the front sprocket diameter of the wheels angular rate length of pedal cranks diameter of the sprocket none of these

Explanation / Answer

Wheel diameter (Dw) = 67.3 cmCrank diameter (Dc) = 35 cmAngular velocity () = 72.0 rev/min = 1.2 rev/s = 432°/s = 2.4 rad/sFront sprocket diameter (Df) = 15.2 cm [f = 2.4 rad/s]Rear sprocket diameter (Dr) = 6.00 cm
the speed of a link of the chain relative to the bicycle frame. (m/s) Cf = Df = 47.75 cm = 0.4775 mvf = f x Cf = 1.2 rev/s x 0.4775 m = 0.573 m/s Linear velocity of front sprocket
v = 0.573 m/s Linear velocity of chain link

the angular speed of the bicycle wheels. (rad/s) Dc/Dw = w/c35/67.3 = w/2.467.3(w) = 84w = 84/67.3w = 1.25 rad/s = 3.92rad/s Angular velocity of wheel

Calculate the speed of the bicycle relative to the road. (m/s)Cw = Dw = 2.114 mvw = w x Cw = 0.625 rev/s x 2.114 m = 1.3 m/s Linear velocity of bicycle

d) length of pedal cranks

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