Chapter 8, Problem 81A

To determine

To Explain: The three ways to produce enough torque from your friend.

Explanation of Solution

Introduction:

The torque is the cross product of force and perpendicular distance is

  $\begin{array}{l}\tau =\overrightarrow{r}\times \overrightarrow{F}\\ \tau =rF\sin \theta \widehat{n}\end{array}$

Where angle between force and distance is $\theta$ and $\widehat{n}$ is the direction of the torque.

So, to increase the torque three different ways are-

1. Increase the force applied.

Increase the length of lug wrench $r$ .

Apply the force F at an angle $\theta =90°$ to distance $r$

2. , then torque will be maximum.

Maximum torque

  $\begin{array}{c}{\tau }_{\max }=\left(rF\sin {90}^0\right)\widehat{n}\\ {\tau }_{\max }=rF\sin {90}^0\\ \left(\sin {90}^0=1\right)\\ {\tau }_{\max }=rF\end{array}$

Conclusion:

At $\theta =90°$ the torque will have maximum value and at $\theta =0^0$ it will be zero.