### Understanding the Angle of Repose in Granular MaterialsWhen granular materials fall, they form conical piles. The angle of slope, measured from the horizontal, at which the material comes to rest is called the **angle of repose**. The angle of repose $ \theta $ is related to the height $ h $ and base radius $ r $ of the conical pile by the equation:\[ \theta = \cot^{-1}\left(\frac{r}{h}\right) \]For instance, if granular materials are stored in a pile 10 feet high and the diameter of the base of the pile is 25 feet, you can determine various aspects of the pile using the provided formula.Below the formula, there are some practical exercises:#### (a) Calculating the Angle of Repose**Find the angle of repose for these granular materials:**\[ \theta = \boxed{\phantom{00}}^\circ \](Round to two decimal places as needed.)#### (b) Determining Base Diameter**What is the base diameter of a pile that is 15 feet high?**\[ \text{diameter} = \boxed{\phantom{000}} \text{ feet} \](Round to two decimal places as needed.)#### (c) Finding the Height of the Pile**What is the height of a pile that has a base diameter of approximately 114 feet?**\[ \text{height} = \boxed{\phantom{000}} \text{ feet} \](Round to two decimal places as needed.)### Visual RepresentationThe image includes a diagram of a conical pile illustrating the relationship between the height ($ h $), radius ($ r $), and angle of repose ($ \theta $). The height is shown as a vertical line from the base to the apex of the cone. The radius is the horizontal distance from the center of the base to its edge. The angle of repose ($ \theta $) is represented as the angle between the height line and the sloped surface of the pile.Understanding these relationships is crucial for fields like material science, civil engineering, and geotechnics, where handling and storage of granular materials are common.

Given angle of repose , θ= cot-1 rha) given h=10 ft , d= 25 ft r=…

When granular materials fall, they form conical piles. The angle of slope, measured from the horizontal, at which the material comes to rest is called the angle of repose. The angle of repose is related to the height h and base radius r of the conical pile by the equation 0 = cot -1 When certain h granular materials are stored in a pile 10 feet high, the diameter of the base of the pile is 25 feet.

When granular materials fall, they form conical piles. The angle of slope, measured from the horizontal, at which the material comes to rest is called the angle of repose. The angle of repose is related to the height h and base radius r of the conical pile by the equation 0 = cot -1 When certain h granular materials are stored in a pile 10 feet high, the diameter of the base of the pile is 25 feet.

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter8: Complex Numbers And Polarcoordinates

Section: Chapter Questions

Problem 8CLT

See similar textbooks

Related questions

Q: a plane has an airspeed of 146 km / h. It is flying on a bearing 80 degree while there is 28km/h…

A: Plane speed =146km/h Bearing=80° Wind speed=28km/h

Q: What is the angle that spans this sector

Q: (2x- 1)" n! n3D0

Q: Find the angle of depression of a plane after reaching a height of 203m if its horizontal distance…

A: We have to find the angle of depression of a plane after reaching a height of 203m if its horizontal…

Q: angle of depression from Platform A to Platform B to the nearest tenth.

A: Given: Kara is zip - lining in the forest . She is standing at the top of Platform A ready to zip -…

Q: A line CD is 50 mm long. Endpoints C & D are 20 mm above HP. Endpoint C is 15 mm in-front of VP. The…

A: Draw the projections and trace of the line for quadrant 1 only. First sketch the HP and VP.

Q: Name a point, and identify its coordinates, that is between 20 and 30 units away from point K…

Q: An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50° with the…

A: Given that An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50°…

Q: The front (and back) of a greenhouse have the same shape and dimensions shown below. The greenhouse…

A: Volume of green house will be the total volume of the rectangular and conical portion. Given:…

Q: A flagpole 3m high stands on top of a pedestal 2m high above the ground. At a distance “x” meters…

A: A flagpole 3m high stands on top of a pedestal 2m high above the ground. At a distance “x” meters…

Q: Find the length of the slant height l of a right circular cone with r = 4 cm and h = 6 cm.

A: The slant height l for a right circular cone is calculated by using the formula given below:-l=r2+h2…

Q: A bowling ball is rolled down the alley with a constant velocity of 1.4 m/sec. at an angle of 86° to…

A: Note: According to our expert guidelines only first individual question is to be answered kindly…

Q: an aircraft flying at a height of 400m measures the angle of depression of the end the runaway as…

A: Aircraft lying at height of 400m angle of depression of the end of the runway as 25degree…

Q: Consider a rectangular coordinate system with origin at the center of the earth, z-axis through the…

A: It's easily converted to rectangular coordinate by assuming latitude and longitude as angle over…

Q: The “tropical zone” of the Earth is located approximately between the parallels 30º

Q: The propeller of an airplane has a radius of 3 feet. The propeller is rotating at 2250 revolutions…

A: Given that the radius of propeller (r) = 3 feet The propeller is rotating at 2250 revolutions per…

Question

### Understanding the Angle of Repose in Granular Materials

When granular materials fall, they form conical piles. The angle of slope, measured from the horizontal, at which the material comes to rest is called the **angle of repose**. The angle of repose $ \theta $ is related to the height $ h $ and base radius $ r $ of the conical pile by the equation:

\[ \theta = \cot^{-1}\left(\frac{r}{h}\right) \]

For instance, if granular materials are stored in a pile 10 feet high and the diameter of the base of the pile is 25 feet, you can determine various aspects of the pile using the provided formula.

Below the formula, there are some practical exercises:

#### (a) Calculating the Angle of Repose
**Find the angle of repose for these granular materials:**

\[ \theta = \boxed{\phantom{00}}^\circ \]
(Round to two decimal places as needed.)

#### (b) Determining Base Diameter
**What is the base diameter of a pile that is 15 feet high?**

\[ \text{diameter} = \boxed{\phantom{000}} \text{ feet} \]
(Round to two decimal places as needed.)

#### (c) Finding the Height of the Pile
**What is the height of a pile that has a base diameter of approximately 114 feet?**

\[ \text{height} = \boxed{\phantom{000}} \text{ feet} \]
(Round to two decimal places as needed.)

### Visual Representation

The image includes a diagram of a conical pile illustrating the relationship between the height ($ h $), radius ($ r $), and angle of repose ($ \theta $). The height is shown as a vertical line from the base to the apex of the cone. The radius is the horizontal distance from the center of the base to its edge. The angle of repose ($ \theta $) is represented as the angle between the height line and the sloped surface of the pile.

Understanding these relationships is crucial for fields like material science, civil engineering, and geotechnics, where handling and storage of granular materials are common.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Spheres$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.

Similar questions

Use the analytic method to decide what type of triangle is formed when the midpoints of the sides of an isosceles triangle are joined by line segments.
Write a G-code program for the counterclockwise arc with starting point (-40, -20), ending point (30, -90), and center at (80, 30), where units are in millimeters.
Find the exact distance between (5,3)and(2,8) . Find the coordinates of the midpoint of the line segment joining the two points.
Point P is rotated 210° counterclockwise around a circle with a diameter of 20 meters. If the center of the circle is at the origin, which coordinates represent the location of P' relative to the center? A (-5/3,-5) 210° (-10/3,-10) C (-10,–10/3) D (-5, -5/3)
Angle EFG has a measure of 133°. Triangle EFG is rotated 180° counterclockwise about point F to create triangle E'FG'. What is the measure of angle E'F'G' ?
Point C (-5, 4) is reflected over the X-axis. What are the coordinates of C'? 4. O a) (5, 4) O b) (-5, -4) O c) (5, -4) O d) (-5, 4) hp & 24 8. 4. *00 %#3