Question

A bicyclist of mass $\mathbf{70}\mathbf{}\mathit{k}\mathit{g}$ puts all his mass on each downward moving pedal as he pedals up a steep road. Take the diameter of the circle in which the pedals rotate to be$\mathbf{0}\mathbf{.}\mathbf{40}\mathit{m}$ , and determine the magnitude of the maximum torque he exerts about the rotation axis of the pedals.

Short answer

Magnitude of maximum torque is $140\text{N}.\text{m.}$

Step-by-step solution

Step 1: Given

1. Mass of the bicyclist is $70\text{kg}$
2. Diameter of the circle in which the pedal rotates is $0.40\text{m}$

Determining the concept

Firstly, find the force from mass and acceleration due to gravity. Then, using the formula for torque in terms of force and radius, find the torque.

Formulae are as follow:

$$\begin{gathered} \tau =r\times F \\ F=mg \end{gathered}$$

Where,

$\tau$ is torque, m is mass, r is radius, F is force and g is acceleration due to gravity.

Determining the magnitude of maximum torque

First, find force as follows:

$$\begin{gathered} F=m\times g \\ F=70\times 9.8 \\ F=686\text{N} \end{gathered}$$

Now, torque is found as follows:

$$\begin{gathered} \tau =F\times \frac{d}{2} \\ \tau =686\times \frac{0.4}{2} \\ \tau =137.2\text{N}.\text{m} \end{gathered}$$

In two significant figures,

$\tau =140\text{N}.\text{m}$

Hence, magnitude of maximum torque is $140\text{N}.\text{m}$

Therefore, the formula for torque in terms of force and radius can be found to find the torque about the rotational axis of the pedals.