Chapter 4.7, Problem 101E

(a)

To determine

The angle of repose for the rock salt

Answer to Problem 101E

The angle of response for rock salt is approx. ${33}^{\circ }$

Explanation of Solution

Given information:

Find the angle of response for rock salt and how tall is a pile of rock salt that has a base diameter of 20 meters.

The given graph:

  

Formula used:

  $\tan \theta =\frac{OB}{OA}$

Calculation:

Here,

  $OA=8.5\text{and}OB=5.5$ Use the tangent formula in triangle AOB

  $\begin{array}{l}\tan \theta =\frac{OB}{OA}\\ =\frac{5.5}{8.5}\\ \theta =\arctan \left(\frac{5.5}{8.5}\right)\\ \theta ={33}^{\circ }\end{array}$

Thus, the angle of response for rock salt is approx. ${33}^{\circ }$

Conclusion:

The angle of response for rock salt is approx. ${33}^{\circ }$

(b)

To determine

The height of the pile of rock salt that has base diameter of 20 meters.

Answer to Problem 101E

The value is approx. 6.5m tall is a pile of rock salt that has a base diameter of 20 meters

Explanation of Solution

Given information:

Find the angle of response for rock salt and how tall is a pile of rock salt that has a base diameter of 20 meters.

The given graph:

  

Formula used:

  $\tan \theta =\frac{OB}{OA}$

Calculation:

When rock salt has a base diameter of 20 meters so, $OA=\frac{20}{2}=10$ . Use the angle of part (a) and have

  $\begin{array}{l}\tan \theta =\frac{OB}{OA}\\ \tan {33}^{\circ }=\frac{OB}{10}\\ \frac{5.5}{8.5}10=OB\\ OB=6.5\end{array}$

Thus, approx. 6.5m tall is a pile of rock salt that has a base diameter of 20 meters.

Conclusion:

The value is approx. 6.5m tall is a pile of rock salt that has a base diameter of 20 meters