A bicycle wheel has a radius R = 32.0 cm and a mass M = 1.82 kg which you may as

Question

A bicycle wheel has a radius R = 32.0 cm and a mass M = 1.82 kg which you may assume to be concentrated on the outside radius. A resistive force f = [07] N (due to the ground) is applied to the rim of the tire. A force F is applied to the sprocket at radius r such that the wheel has an angular acceleration of = 4.50 rad/s2 . The tire does not slip.

(a) If the sprocket radius is 4.53 cm, what is the force F (N)?

(b) If the sprocket radius is 2.88 cm, what is the force F (N)?

(c) What is the combined mass of the bicycle and rider (kg)?

Explanation / Answer

A) net torque = Tnet = I*alpha = (m*r^2)*alpha = (1.82*0.32*0.32*4.5) = 0.8386

Tnet = (r*F)-(147*0.32)

r*F = 47.04+0.8386

r= 0.453 m

F = 1056.9 N

B) r*F = 47.04+0.8386

r = 0.0288 m

F = 47.8786/0.0288 = 1662.45 N

C)
mass m = F/a = 147/(R*alpha) 147/(0.32*4.5) = 102 kg

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