Question

a bicycle wheel has a diameter of 64.8 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 122 n is applied tangent to the rim of the tire. (a) what force must be applied by a chain passing over a 9.04-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 5.70-cm-diameter sprocket?

Answer 1

To find the force required by a chain passing over a 9.04-cm-diameter sprocket and a 5.70-cm-diameter sprocket to give the wheel an acceleration of 4.52 rad/s².

This question involves the concept of rotational motion and torque. To find the force required by a chain passing over a 9.04-cm-diameter sprocket to give the wheel an acceleration of 4.52 rad/s², we can use the equation:

Torque = Moment of Inertia x Angular Acceleration

The moment of inertia of the wheel can be calculated using the formula for the moment of inertia of a hoop:

Moment of Inertia = mass x radius²

Once we have the moment of inertia, we can rearrange the torque equation to solve for the force:

Force = Torque / Radius

Using the given values, we can substitute them into the equations and calculate the force required.

For the second part of the question, the same process can be followed using the given diameter of the new sprocket to find the force required.