A bicycle wheel has radius R = 32.0 cm and mass M = 1.82 kg which you may assume

Question

A bicycle wheel has radius R = 32.0 cm and mass M = 1.82 kg
which you may assume to be concentrated on the outside radius.
A resistive force f = 100 N (due to friction with the
ground) is applied to the rim of the tire. A force F is applied to
the sprocket at radius r by the bicycle chain such that the wheel
has an angular acceleration of alpha(a) = 4.50 rad/s2. The tire does not
slip with the ground, and the lower part of the chain (not shown)
exerts no force.
What is the combined mass of the bicycle and rider?
Hint: The force F also acts on
the front sprocket of the bicycle.

Please Answer with the approriate Steps THANK YOU

Explanation / Answer

a) If the sprocket radius is 4.53 cm, what is the force F (N)?

(mr^2)(4.5) = (r)(F)- (100)(.32)
(1.82)(.32^2)(4.5) = (.0453)(F)-(100)(.32)

F = (0.838656 + 32)/0.0453
F= 724.915 N

b) If the sprocket radius is 2.88 cm, what is the force F(N)?

(1.82)(.32^2)(4.5) = (.0288)(F)-(100)(.32)

F = (0.838656 + 32)/0.0288 = 1140.23

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