Chapter 9, Problem 115RE

To determine

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

Answer to Problem 115RE

The required force is $7969.6\text{lb}$ .

Explanation of Solution

Given:

The weight of the van is $8000$ pounds.

The incline angle is of $5°$

Calculation:

Consider the diagram for the given case is shown in Figure 1

Figure 1

Consider the gravitational force is $F_1$ , force required to move the van down is $F_2$ and the force of the van against the hill is $F_3$ .

Consider the angle relation as,

  $\angle BAC=\angle DBE$

Then,

  $\sin 5°=\left|\frac{F_2}{F_1}\right|$

Then,

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

  $F_3$ is the force against the hill and is perpendicular to the hill so,

  $\begin{array}{l}\cos 5°=\frac{\left|F_3\right|}{\left|F_1\right|}\\ 0.9962=\frac{F_3}{8000}\\ F_3=8000\times 0.9962\\ F_3=7969.6\text{lb}\end{array}$