A bicycle wheel has a diameter of 64.2 cm and a mass of 1.84 kg. Assume that the

Question

A bicycle wheel has a diameter of 64.2 cm and a mass of 1.84 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 116 N is applied tangent to the rim of the tire.

(a) What force must be applied by a chain passing over a 8.98-cm-diameter sprocket in order to give the wheel an acceleration of 4.46 rad/s2?
? N

(b) What force is required if you shift to a 5.64-cm-diameter sprocket?
? N

Explanation / Answer

a) net torque =116*.321 -F*.0449 =37.236 -.0449F
net acceleration = 4.46 =(37.236-.0449F)/1.84*(.321)^2
solving, we get, F=810.5N

b)similar treatment of the question, yields , F=1290.4N

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