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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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**Educational Website Content:** --- **1. State Newton's first law.** Newton's First Law of Motion states that an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force. Similarly, an object at rest remains at rest unless acted upon by an unbalanced external force. --- **2. Diagram Analysis** The diagram consists of a horizontal beam labeled "D," subjected to forces at specific points. The following details describe the scenario: - An upward force of 1000 lbs is applied at the left end of the beam. - The beam has a length of 20 feet, divided into two 10-foot sections. - At the right end of the beam, a downward force of 2000 lbs and a rightward force of 300 lbs are applied. *Objective: Find the sum of moments about point D, denoted as \(\Sigma \overrightarrow{M}_D\).* --- **3. Diagram Analysis** The diagram shows an L-shaped structure with the following details: - Two vertical sections labeled "L" at the top and bottom, with a height of 2 meters each. - Three horizontal sections labeled "L," "L," and "2m" with equal spacing of "m". - Point "O" is located at the bottom-left corner, with points labeled "O" and "C". *Objective: Find the position vector \(\overrightarrow{r}_{OC}\).* --- **4. Diagram Analysis** The diagram shows a horizontal beam fixed at one end, labeled "A," with forces applied: - Two upward forces of 1000 lbs each are applied at points "B" and "C," both spaced at 5 feet intervals from each other. - The section distance from point "A" to "B" is 5 feet. *Objective: Find the reaction at point A.* --- **Notes:** - All diagrams include \(\hat{i}\) and \(\hat{j}\) vectors, representing horizontal and vertical axes, respectively. - Calculations involving forces and moments must consider the principles of static equilibrium: summation of forces and moments must equal zero for systems in equilibrium. ---
Transcribed Image Text:**Educational Website Content:** --- **1. State Newton's first law.** Newton's First Law of Motion states that an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force. Similarly, an object at rest remains at rest unless acted upon by an unbalanced external force. --- **2. Diagram Analysis** The diagram consists of a horizontal beam labeled "D," subjected to forces at specific points. The following details describe the scenario: - An upward force of 1000 lbs is applied at the left end of the beam. - The beam has a length of 20 feet, divided into two 10-foot sections. - At the right end of the beam, a downward force of 2000 lbs and a rightward force of 300 lbs are applied. *Objective: Find the sum of moments about point D, denoted as \(\Sigma \overrightarrow{M}_D\).* --- **3. Diagram Analysis** The diagram shows an L-shaped structure with the following details: - Two vertical sections labeled "L" at the top and bottom, with a height of 2 meters each. - Three horizontal sections labeled "L," "L," and "2m" with equal spacing of "m". - Point "O" is located at the bottom-left corner, with points labeled "O" and "C". *Objective: Find the position vector \(\overrightarrow{r}_{OC}\).* --- **4. Diagram Analysis** The diagram shows a horizontal beam fixed at one end, labeled "A," with forces applied: - Two upward forces of 1000 lbs each are applied at points "B" and "C," both spaced at 5 feet intervals from each other. - The section distance from point "A" to "B" is 5 feet. *Objective: Find the reaction at point A.* --- **Notes:** - All diagrams include \(\hat{i}\) and \(\hat{j}\) vectors, representing horizontal and vertical axes, respectively. - Calculations involving forces and moments must consider the principles of static equilibrium: summation of forces and moments must equal zero for systems in equilibrium. ---
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