A bicycle wheel has a diameter of 63.7 cm and a mass of 1.83 kg. Assume that the
ID: 1474345 • Letter: A
Question
A bicycle wheel has a diameter of 63.7 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 125 N is applied tangent to the rim of the tire.
(a) What force must be applied by a chain passing over a 9.10 cm diameter sprocket if the wheel is to attain an acceleration of 4.47 rad/s2?__________N
(b) What force is required if the chain shifts to a 5.50 cm diameter sprocket?___________ N
Explanation / Answer
A bicycle wheel has a diameter of 63.7 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 125 N is applied tangent to the rim of the tire.
(a) What force must be applied by a chain passing over a 9.10 cm diameter sprocket if the wheel is to attain an acceleration of 4.47 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 0.316^2 = 0.18273 kg-m^2
Torque = 0.18273 x 4.47= 0.816 Nm
0.816/radius = force
0.816/0.0446 = 18.83 N
What force must be applied to attain acc of 4.47 rad/s^2?
18.83 N
125 N x 0.316 m = 39.5 Nm
39.5/ 0.0446 = 85.56 N
Total = 18.83 + 85.56 = 104.839N (answer)
(b) What force is required if the chain shifts to a 5.50 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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