The figure below shows the drive train of a bicycle that has wheels 67.3 cm in d
ID: 1349470 • Letter: T
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.
(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.)diameter of front sprocket
b.)diameter of wheels
c.)angular rate
d.)length of pedal cranks
e.)diameter of rear sprocket
f.)none of these
Explanation / Answer
here,
Dw = 67.3 = 0.673 m
Dc = 0.35
Wc = 73.5 rev/min = 7.697 rad/s
front sprocket = Dfs = 15.2cm = 0.152 m
rear sprocket = Drs = 7 cm = 0.07 m
A)
Cf = 3.14 * 0.152
Cf = 0.517 m
Vf = wf *Cf
Vf = 73.5 * 0.517
Vf = 38 m/s
Calculate the speed of a link of the chain relative to the bicycle frame is 38 m/s
B)
Dc/Dw = W/Wc
W = (Dc/Dw) * Wc
W = (0.35/0.673) * 7.697
W = 4.002 rad/s
Calculate the angular speed of the bicycle wheels 4.002 rad/s
C)
Cw = pi*Dw = 3.14 * 0.673 = 2.113 m
Vw = W * Cw
w = 4.002 * 2.113
w = 8.456 m/s
Calculate the speed of the bicycle relative to the road 8.456 m/s
D)
Didn't need crank length.