Chapter 8.5, Problem 6CFU

To determine

To find: the magnitude and direction of the resultant force and 50 pound force.

Answer to Problem 6CFU

Magnitude: 111.8 N

Direction: $63.43°$

Explanation of Solution

Given information:

Let the components be $\overrightarrow{F_1}\text{ and }\overrightarrow{F_2}$ .

  $\begin{array}{c}\overrightarrow{F_1}=50\overrightarrow{i}\\ \overrightarrow{F_2}=100\overrightarrow{j}\\ \theta =90°\end{array}$

Calculation:

Take 50 N directing towards $\left(+x\right)$ . The magnitude of the resultant vector is evaluated as follows:

  $\begin{array}{c}\left|\overrightarrow{F_1}+\overrightarrow{F_2}\right|=\sqrt{{\left(50\right)}^2+{\left(100\right)}^2}\\ =\sqrt{25000+10000}\\ \approx 111.8\text{ N}\end{array}$

The direction of the resultant vector is evaluated as follows:

  $\begin{array}{c}\tan \theta =\frac{100}{50}\\ \theta ={\tan }^{-1}\left(\frac{100}{50}\right)\\ ={\tan }^{-1}\left(2\right)\\ \approx 63.43°\end{array}$

Thus the magnitude and direction of resultant vector is 111.8 N and $63.43°$ respectively.