Chapter 8.2, Problem 14PP

To determine

The torque exerted on the bicycle by a person if the pedal length from the center of the chain ring is $18\text{cm}$ .

Answer to Problem 14PP

  $93.92\text{N}\cdot \text{m}$

Explanation of Solution

Given:

The mass of the person riding the bicycle, $m=65\text{kg}$

The pedal length from the center of the chain ring, $r=18\text{cm}=\text{0}\text{.18 m}$

The angle made by the pedal above the horizontal, $\varphi =35°$

Formula used:

The torque is given 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:

When the person stands on the pedal, only force acting on the pedal is due to the weight of the person only. And the angle between the pedal length from the center of the chain ring and the weight of the person will be $\theta =\left(90°-35°\right)$ .

Then, using the formula of torque,

  $\begin{array}{c}\tau =Fr\sin \theta \\ =\left(mg\right)\left(r\right)\sin \left(90°-35°\right)\\ =\left(65\right)\left(9.8\right)\left(0.18\right)\cos 35°\\ =93.92\text{N}\cdot \text{m}\end{array}$

Conclusion:

Thus, the torque exerted on the bicycle is $93.92\text{N}\cdot \text{m}$ .