A bicycle wheel has a diameter of 65.0 cm and a mass of 1.83 kg. Assume that the

Question

A bicycle wheel has a diameter of 65.0 cm and a mass of 1.83 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 119 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 8.92-cm-diameter sprocket in order to give the wheel an acceleration of 4.57 rad/s2? _____ N (b) What force is required if you shift to a 5.69-cm-diameter sprocket? _____ N

Explanation / Answer

A bicycle wheel has a diameter of 65 cm and a mass of 1.83 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 119 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 8.92 cm diameter sprocket if the wheel is to attain an acceleration of 4.57 rad/s2? in N Torque = Inertia x alpha (angular acceleration rad/s^2) Torque also equals force x radius First of all lets find the inertia of the wheel. hoop = mr^2 = 1.83 x 0.325^2 = 0.1932 kg-m^2 Torque = 0.1932 x 4.57 = 0.8829 Nm 0.8829/radius = force 0.8829/0.0446 = 19.79 N What force must be applied to attain acc of 4.5 rad/s^2? 19.79 N 119 N x 0.325 m = 38.675 Nm 38.675/ 0.0446 = 871.48 N Total = 17.33 + 871.48 = 867.15 N (answer) (b) What force is required if the chain shifts to a 5.69 cm diameter sprocket? I should let you do this yourself. Hint: the Torque is the same and divide by the radius (m's)

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