Chapter 8.5, Problem 7CFU

To determine

To find: the horizontal and vertical components of the forces.

Answer to Problem 7CFU

Horizontal component: 13.79 N

Vertical component: 11.57 N

Explanation of Solution

Given information:

  $\begin{array}{c}\left|\overrightarrow{r}\right|=18\text{ N}\\ \theta =40°\end{array}$

Calculation:

Let the horizontal and vertical components be $\overrightarrow{F_1}\text{ and }\overrightarrow{F_2}$ respectively. The diagram for the given situation is as follows:

  

The components of the vector are evaluated as follows:

  $\begin{array}{c}\overrightarrow{F_1}=\left|\overrightarrow{r}\right|\cos \theta \\ =18\cos 40°\\ =13.79\text{ N}\\ \overrightarrow{F_2}=\left|\overrightarrow{r}\right|\sin \theta \\ =18\sin 40°\\ =11.57\text{ N}\end{array}$

Thus the horizontal and vertical component of the force is 13.79 N and 11.57 N respectively.