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3.5 m r= 0.6e-0.08y² y 0.6 m

3.5 m r= 0.6e-0.08y² y 0.6 m

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A unique column has been created with the geometry shown below, where the radius is r = (0.6e-0.08y2) m, the variable y is in meters. The column density of the column material is ρ = 3.21 Mg/m3. Determine the average normal stress at the bottom of the column (y = 0) in units of Pa.

### Conical Object with Variable Radius This diagram represents a three-dimensional conical object with a variable radius, where the radius changes based on the height from the base. #### Dimensions and Formula - **Height of Cone (H):** 3.5 meters - **Base Diameter (D):** 0.6 meters The radius \( r \) of the cone at any height \( y \) from the base is defined by the function: \[ r = 0.6 e^{-0.08y^2} \] #### Components 1. **Height (H):** The vertical distance from the base to the top of the cone is 3.5 meters. 2. **Base Diameter (D):** The diameter at the base of the cone is 0.6 meters. 3. **Height Variable (y):** A variable representing the height from the base to any given point along the cone. 4. **Radius Function \( r(y) \):** The radius \( r \) at a specific height \( y \) from the base is given by the function \( r = 0.6 e^{-0.08y^2} \). This model is typically used to study objects whose radius changes exponentially with height. Analyzing such a model can help in understanding various natural and engineering processes, such as fluid dynamics in conical vessels, structural integrity of conical beams, or other practical applications involving variable-radius cones. **Notes on Visualization:** - The shading and texture in the diagram indicate the conical shape and changing radius. - The exponential decay in the radius is visually represented, getting narrower as it approaches the top. This conical model can serve as a practical example in various fields, including mathematics, physics (for studying properties of solids of revolution), and engineering (for practical design and structural analysis).
Transcribed Image Text:### Conical Object with Variable Radius This diagram represents a three-dimensional conical object with a variable radius, where the radius changes based on the height from the base. #### Dimensions and Formula - **Height of Cone (H):** 3.5 meters - **Base Diameter (D):** 0.6 meters The radius \( r \) of the cone at any height \( y \) from the base is defined by the function: \[ r = 0.6 e^{-0.08y^2} \] #### Components 1. **Height (H):** The vertical distance from the base to the top of the cone is 3.5 meters. 2. **Base Diameter (D):** The diameter at the base of the cone is 0.6 meters. 3. **Height Variable (y):** A variable representing the height from the base to any given point along the cone. 4. **Radius Function \( r(y) \):** The radius \( r \) at a specific height \( y \) from the base is given by the function \( r = 0.6 e^{-0.08y^2} \). This model is typically used to study objects whose radius changes exponentially with height. Analyzing such a model can help in understanding various natural and engineering processes, such as fluid dynamics in conical vessels, structural integrity of conical beams, or other practical applications involving variable-radius cones. **Notes on Visualization:** - The shading and texture in the diagram indicate the conical shape and changing radius. - The exponential decay in the radius is visually represented, getting narrower as it approaches the top. This conical model can serve as a practical example in various fields, including mathematics, physics (for studying properties of solids of revolution), and engineering (for practical design and structural analysis).
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