Chapter 8.2, Problem 13PP

a.

To determine

The smallest angle.

Answer to Problem 13PP

Smallest angle will be equal to $\theta =36.64°$ .

Explanation of Solution

Given :

Length of the wrench, $l=0.234\text{ m}$

Torque requires, $\tau =32.4\text{ N-m}$

Force exerted, $F=232\text{ N}$

Formula used :

  $\tau =Fl\sin \theta$

Here, $\tau$ is torque, F is force, l is length and $\theta$ is the angle between force exerted and handle.

Calculation :

Now, substitute the value of $\tau$ , F and l .

  $\begin{array}{c}32.4=232\times 0.234\times \sin \theta \\ \sin \theta =0.5968\\ \theta ={\sin }^{-1}\left(0.5968\right)\\ =36.64°\end{array}$

Conclusion :

Therefore, smallest angle will be equal to $36.64°$ .

b.

To determine

The smallest angle.

Answer to Problem 13PP

Smallest angle will be equal to $\theta =30.23°$

Explanation of Solution

Given :

Length of the wrench, $l=0.234\text{ m}$

Torque requires, $\tau =32.4\text{ N-m}$

Force exerted, $F=275\text{ N}$

Formula used :

  $\tau =Fl\sin \theta$

Here, $\tau$ is torque, F is force, l is length and $\theta$ is the angle between force exerted and handle.

Calculation :

Now, substitute the value of $\tau$ , F and l .

  $\begin{array}{c}32.4=275\times 0.234\times \sin \theta \\ \sin \theta =0.5034\\ \theta ={\sin }^{-1}\left(0.5034\right)\\ =30.23°\end{array}$

Conclusion :

Therefore, smallest angle will be equal to $30.23°$ .