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

Answer 1

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