A bicycle wheel has a diameter of 64.2 cm and a mass of 1.85 kg. Assume that the

Question

A bicycle wheel has a diameter of 64.2 cm and a mass of 1.85 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 4.54 rad/s2?
N

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

PLEASE EXPLAIN STEPS

Explanation / Answer

Here ,

let the force on the sproket is F

moment of inertia of wheel , I = m * r^2

I = 1.85 * (0.642/2)^2

I = 0.191 Kg.m^2

Using second law of motion

F * (0.0898/2) - 116 * (0.642/2) = 0.191 * 4.54

F = 848.6 N

the force must be applied is 848.6 N

b)

for the force shifted is 5.64 cm

Using second law of motion

F * (0.0564/2) - 116 * (0.642/2) = 0.191 * 4.54

F = 1351.2 N = 1.35 kN

the force must be applied is 1.35 kN

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