A bicycle wheel has a diameter of 64.2 cm and a mass of 1.78 kg. Assume that the

Question

A bicycle wheel has a diameter of 64.2 cm and a mass of 1.78 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 117 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 9.10-cm-diameter sprocket in order to give the wheel an acceleration of 4.47 rad/s2? Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. N (b) What force is required if you shift to a 5.62-cm-diameter sprocket? 843 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. kN

Explanation / Answer

angular acceleration of wheel = angular acceleration of sprocket = 4.47 rad/s^2

net torque = I*alpha

(F*Rsprocket) - (Fr*Rwheel) = Iwheel*alpha

Iwheel = M*Rwheel^2

(F*0.091/2) - (117*0.642/2) = 1.78*(0.642/2)^2*4.47

F = 843.45 N

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(b)

net torque = I*alpha

(F*Rsprocket) - (Fr*Rwheel) = Iwheel*alpha

Iwheel = M*Rwheel^2

(F*0.0562/2) - (117*0.642/2) = 1.78*(0.642/2)^2*4.47

F = 1365.7 N

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