   Chapter 8, Problem 44P

Chapter
Section
Textbook Problem

A bicycle wheel has a diameter of 64.0 cm and a mass of 1.80 kg. Assume that the wheel is a hoop with all the mass concentrated on the outside radius. The bicycle is placed on a stationary stand, and a resistive force of 120 N is applied tangent to the rim of the tire. (a) What force must be applied by a chain passing over a 9.00-cm-diameter sprocket to give the wheel an acceleration of 4.50 rad/s2? (b) What force is required if you shift to a 5.60-cm -diameter sprocket?

(a)

To determine
The force must be applied by a chain passing over a sprocket to give the wheel an acceleration of 4.50rad/s2 .

Explanation

Given info: The mass of the wheel is 1.80kg , the diameter of the wheel is 64.0cm , the resistive force is 120N , the angular acceleration of the wheel is 4.50rad/s2 , and the diameter of the sprocket is 9.00cm .

Explanation: The net torque of the sprocket is τnet=τappliedτresistive=Iα and further it is modified as rFRf=Iα . Now the moment of inertia of the bicycle wheel is I=MR2 and by using these relations, the force that must applied by the chain is found.

The formula for the force must be applied by the chain is,

F=MR2α+Rfr

• M is mass of the wheel.
• R is radius of the wheel.
• α is angular acceleration of the wheel.
• f is resistive force.
• r is radius sprocket.

Substitute 1.80kg for M , 64.0cm/2 for R , 120N for f , 9.00cm/2 for r , and 4.50rad/s2 for α to find F

(b)

To determine
The force must be applied by a chain passing over a sprocket with diameter of 5.60cm to give the wheel an acceleration of 4.50rad/s2 .

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