A bicycle wheel has a diameter of 63.2 cm and a mass of 1.78 kg. Assume that the

Question

A bicycle wheel has a diameter of 63.2 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 120 N is applied tangent to the rim of the tire.


(a) What force must be applied by a chain passing over a 8.99 cm diameter sprocket if the wheel is to attain an acceleration of 4.54 rad/s2?
________N

(b) What force is required if the chain shifts to a 5.68 cm diameter sprocket?
________N

Explanation / Answer

a).T = Ia T - Torque a - angular acceleration F1 r1 - F2 r2 = 1/2 m r^2 x 4.5 (F x 0.09/2) - ( 120 x 0.64/2) = 0.5 x 1.8 x (0.64/2)^2 x 4.5 0.045 F - 38.4 = 0.41472 F = 862.5493 N b).he Torque is the same and divide by the radius (m's) Your answer should be 1390.9 N

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