Chapter 9.5, Problem 32AYU

Incline Angle A bulldozer exerts 1000 pounds of force to prevent a 5000-pound boulder from rolling down a hill. Determine the angle of inclination of the hill.

To determine

To find: The angle of inclination of the hill.

Answer to Problem 32AYU

Solution:

${11.53}^{\circ }$

Explanation of Solution

Given:

A bulldozer exerts 1000 pounds of force to prevent a 5000-pound boulder from rolling down a hill.

Calculation:

The boulder is exerting a 5000 pound force downward, which can be broken into a component parallel to the hill (1000 pounds), and a force normal to the hill.

If you diagram the forces on the boulder, you can see that the parallel force is the total force times the sine of the angle of incline.

$1000=5000\sin \theta$

$\sin \theta =\frac{1}{5}$

$\theta ={\sin }^{-1}\left(\frac{1}{5}\right)={11.53}^{\circ }$