Chapter 4.7, Problem 107E

a.

To determine

Find the angle of repose for whole corn.

Answer to Problem 107E

  $\boxed{26.0°}$

Explanation of Solution

Given information:

When whole corn is stored in a cone-shaped pile $20$ feet high, the diameter of the pile’s base is about $82$ feet.

Find the angle of repose for whole corn.

Calculation:

Let us consider the following figure

  We shall find the angle of repose of the whole corn

Hence,

We shall take the tangent of the angle

  $\begin{array}{l}\tan \theta =\frac{20}{41}\\ \theta =\arctan \left(\frac{20}{41}\right)\approx 26.0°\end{array}$

Hence the angle of repose is $26.0°$

b.

To determine

How tall is a pile of corn that has a base diameter of $100$ feet?

Answer to Problem 107E

  $\boxed{24.4feet}$

Explanation of Solution

Given information:

When whole corn is stored in a cone-shaped pile $20$ feet high, the diameter of the pile’s base is about $82$ feet.

How tall is a pile of corn that has a base diameter of $100$ feet?

Calculation:

Let us consider the following figure

  

We shall take tangent of anle using radius of $50$ feet

Hence,

  $\begin{array}{l}\tan 26°=\frac{h}{50}\\ h=50\tan 26°\approx 24.4feet\end{array}$