i keep trying to get this but my calculations are off! HELP A bicycle wheel has

Question

i keep trying to get this but my calculations are off! HELP

A bicycle wheel has a diameter of 65.0 cm and a mass of 1.79 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 118 N is applied tangent to the rim of the tire.

(a) What force must be applied by a chain passing over a 8.94-cm-diameter sprocket in order to give the wheel an acceleration of 4.52 rad/s2?
N

(b) What force is required if you shift to a 5.51-cm-diameter sprocket?
N

Explanation / Answer

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 = 1.72 x 0.316^2 = 0.17175 kg-m^2

Torque = 0.17175 x 4.5 = 0.7729 Nm

0.7729/radius = force
0.7729/0.0446 = 17.33 N

What force must be applied to attain acc of 4.5 rad/s^2?

17.33 N

123 N x 0.316 m = 38.868 Nm

38.868/ 0.0446 = 871.48 N

Total = 17.33 + 871.48 = 888.8 N (answer)

(b) What force is required if the chain shifts to a 5.70 cm diameter sprocket?

I should let you do this yourself.

Hint: the Torque is the same and divide by the radius (m's)

Your answer should be 1390.9 N

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