A bicycle wheel has a diameter of 64.6 cm and a mass of 1.87 kg. Assume that the

Question

A bicycle wheel has a diameter of 64.6 cm and a mass of 1.87 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 121 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 4.42 rad/s^2? ________ N.

b) What force is required if you shift to a 5.53 cm diameter sprocket? __________ kN.

Explanation / Answer

a. moment of inertia = MR^2 = 1.87 x 0.323^2= 0.195 kg.m^2

net torque required = 0.195 x 4.42= 0.862 N.m

If Fis the force then 0.862 = 121 x0.323 - F x0.0449

so, F = 851.24 N

b. then 0.862 = 121x0.323 - F x 0.0276

so, F=1384.81 N= 1.384 Kn

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