Chapter 7.2, Problem 83AYU

Problems 79 and 80 require the following discussion: When granular materials are allowed to fall freely, they form conical (cone-shaped) piles. The naturally occurring angle of slope, measured from the horizontal, at which the loose material comes to rest is called the angle of repose and varies for different materials. The angle of repose $\theta$ is related to the height $h$ and base radius $r$ of the conical pile by the equation $\theta ={\cot }^{-1}\frac{r}{h}$. See the illustration.

Angle of Repose: Deicing Salt Due to potential transportation issues (for example, frozen waterways) deicing salt used by highway departments in the Midwest must be ordered early and stored for future use.

When deicing salt is stored in a pile 14 feet high, the diameter of the base of the pile is 45 feet.

(a) Find the angle of repose for deicing salt.

(b) What is the base diameter of a pile that is 17 feet high?

(c) What is the height of a pile that has a base diameter of approximately 122 feet?

Source: The Salt Storage Handbook, 2013