Chapter 11, Problem 35A

When you pedal a bicycle, maximum torque is produced when the pedal sprocket arms are in the horizontal position, and no torque is produced when they are in the vertical position. Explain.

To determine

To Explain:The maximum torque is produced when the pedal sprocket arms are in the horizontal position, and no torque is produced when they are in vertical position.

Explanation of Solution

Introduction:

Mechanics is the branch of physics which describes the motion of object. In case of bicycle riding, crucial part is to apply the correct forces on the pedal. Torque is the twisting force applied on the body when body is under the action of pair of force. Torque can be defined as cross product of force acting on one of the terminals ends of the lever arm and distance of lever arm. While riding the bicycle, torque is changing on each and every point. Mathematically it can be written as,

  $\overrightarrow{\tau }=\overrightarrow{F}\times \overrightarrow{r}\mathrm{...}\left(1\right)$

Where, F is the force, r is the moment arm and ? is the angle between F and r .

Direction of the torque depends on the F and r .

The sprocket of the pedal in the vertical direction. In this case the direction of the applied force and the moment of the arm are in the same direction. So, the angle between them is $0°$ . From equation (1), net torque acting on pedal is,

  $\begin{array}{l}\overrightarrow{\tau }=\overrightarrow{F}\times \overrightarrow{r}\\ \tau =\left|\overrightarrow{F}\right|\left|\overrightarrow{r}\right|\sin \left(\theta \right)\\ \text{Since}\theta =0^0\\ \tau =\left|\overrightarrow{F}\right|\left|\overrightarrow{r}\right|\sin \left(0^0\right)\\ \tau =0\mathrm{...}\left(2\right)\end{array}$

When the sprocket of the pedal in the horizontal direction,the angle between the applied force and the moment of the arm is the $90°$ . From equation (1) we get net torque acting on pedal,

  $\begin{array}{l}\overrightarrow{\tau }=\overrightarrow{F}\times \overrightarrow{r}\\ \tau =\left|\overrightarrow{F}\right|\left|\overrightarrow{r}\right|\sin \left(\theta \right)\\ \text{Since}\theta ={90}^0\\ \tau =\left|\overrightarrow{F}\right|\left|\overrightarrow{r}\right|\sin \left({90}^0\right)\\ \tau =\left|\overrightarrow{F}\right|\left|\overrightarrow{r}\right|\mathrm{...}\left(3\right)\end{array}$

Conclusion:

Therefore, from equation (2) and (3) it can beconcluded that for the maximum torque to begeneratedif the pedal sprocket arms are horizontally positioned, and there is no torque generated if they are in vertical position. Due to the angle between F and r , torque in vertical as well as horizontal direction different.