Chapter 8.2, Problem 17PP

To determine

The torque needed to keep the wheel from turning.

Answer to Problem 17PP

  $2.695\text{N}\cdot \text{m}$ in anticlockwise direction

Explanation of Solution

Given:

The force exerted by chain on the wheel in the clockwise direction, $F=35.0\text{N}$

The radius of a bicycle-chain wheel is $7.70\text{cm}\text{=}\text{0}\text{.077 m}$ .

Formula used:

The torque can be obtained by:

  $\tau =Fr\sin \theta$

Where, F is the applied force, r is the distance of the point of application of force from the axis of rotation, and $\theta$ is the angle between F and r .

Calculation:

The applied force is at angle of $90°$ to the radius of the wheel.

Now, the applied clockwise force will generate torque in clockwise direction. Thus, to stop the wheel from turning, the applied torque should be in anticlockwise direction of the magnitude,

  $\begin{array}{c}\tau =Fr\sin \theta \\ =35\left(0.077\right)\sin 90°\\ =2.695\text{N}\cdot \text{m}\end{array}$

Conclusion:

Thus, the applied torque should be $2.695\text{N}\cdot \text{m}$ in anticlockwise direction.