Chapter 8, Problem 108A

To determine

The angle made by the seesaw with the vertical for the given situation.

Answer to Problem 108A

The value of the angle is $18.43°$ with the vertical.

Explanation of Solution

Given:

The component of weight that is parallel to seesaw length is one-third of the perpendicular component of the weight of the person

Formula used:

The horizontal and vertical component of a force F , if $\theta$ is the angle made with vertical surface, are

  $\begin{array}{l}{F}_x=F\sin \theta \\ F_y=F\cos \theta \end{array}$

Calculation:

Consider the weight of the person E sitting on the seesaw is denoted by $F_{\text{g}}$

Consider the angle made by the seesaw with the vertical is $\theta$ .

The horizontal component and vertical component of the weight of the person E are:

$\begin{array}{l}{F}_{\text{H}}=F_{\text{g}}\sin \theta \\ F_{\text{V}}=F_{\text{g}}\cos \theta \end{array}$

The value of the angle $\theta$ is

$\begin{array}{l}{F}_{\text{H}}=\frac{1}{3}{F}_{\text{V}}\\ F_{\text{g}}\sin \theta =\frac{1}{3}{F}_{\text{g}}\cos \theta \\ \frac{\sin \theta }{\cos \theta }=\left(\frac{1}{3}\right)\\ \tan \theta =\frac{1}{3}\end{array}$

$\begin{array}{l}\theta ={\tan }^{-1}\left(\frac{1}{3}\right)\\ \theta =18.43°\end{array}$

Conclusion:

Thus, the value of the angle is $18.43°$ with the vertical.