Chapter 9, Problem 62RE

To determine

To find: The magnitude of the force required to keep the van from rolling down the hill and the force perpendicular to the hill.

Answer to Problem 62RE

The magnitude of the force required to keep the van from rolling down the hill and the force perpendicular to the hill are $697.2\text{lb}$ and $7969.6\text{lb}$ respectively.

Explanation of Solution

Given information:

The force is $F=8000\text{pounds}$ .

The angles are $\theta =5°$ .

Calculation:

Draw the diagram to show the position of the ramp, van and force applied on it.

  

The above figure shows that the triangle ABC and BDE are similar so $\angle BAC=\angle DBE$

Calculate the magnitude of the force $F_1$ .

  $\begin{array}{c}\sin 5°=\frac{opposite}{hypotenues}\\ \sin 5°=\frac{\left|F_2\right|}{\left|F_1\right|}\\ \left|F_2\right|=8000\text{lb}\left(0.08715\right)\\ \left|F_2\right|=697.2\text{lb}\end{array}$

Apply the cosine function in triangle BED.

  $\begin{array}{c}\cos 5°=\frac{adjacent}{hypotenues}\\ \cos 5°=\frac{\left|F_3\right|}{\left|F_1\right|}\\ \left|F_3\right|=8000\text{lb}\left(0.9962\right)\\ \left|F_3\right|=7969.6\text{lb}\end{array}$

Therefore, the magnitude of the force required to keep the van from rolling down the hill and the force perpendicular to the hill are $697.2\text{lb}$ and $7969.6\text{lb}$ respectively.