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D M M m M M L = 5€ m m m FIG. 2. Find D in the above figure in terms of 0, and L.

D M M m M M L = 5€ m m m FIG. 2. Find D in the above figure in terms of 0, and L.

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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**Title: Analysis of a System of Masses Suspended by Strings** **Figure Description and Instructions:** **Figure 2:** The diagram presents a system of four equal masses \( M \) each suspended by a string of length \( \ell \) from a horizontal support. The equal lengths of string form angles \( \theta_1 \) and \( \theta_2 \) with the vertical axis at different points in the system. **Key Components of the Diagram:** 1. **Angles with Vertical:** - At the points of attachment to the horizontal support, the strings form an angle \( \theta_1 \) with the vertical. - The strings connecting the masses form an angle \( \theta_2 \) with the vertical. 2. **String Lengths:** - The length of each suspending string from the support to the first and last mass is \( \ell \). - The lengths of strings between the masses are also \( \ell \). 3. **Overall Length:** - The total horizontal length spanned by the system of masses is denoted as \( L = 5\ell \). 4. **Horizontal Separation:** - The entire system spans a horizontal distance \( D \), which needs to be expressed in terms of \( \theta_1 \) and \( L \). **Equation to Solve:** The task is to find the total horizontal distance \( D \) in terms of the given angles \( \theta_1 \) and the total length \( L \). **Steps for Solutions:** 1. Decompose the lengths \( \ell \) into horizontal and vertical components using trigonometric functions for \( \theta_1 \) and \( \theta_2 \). 2. Sum the horizontal components to determine the overall horizontal span \( D \). 3. Apply the formula \( L = 5\ell \) to simplify and express \( D \) in terms of \( \theta_1 \) and \( L \). Given these clues and tasks, students are encouraged to use their knowledge of trigonometry to solve for \( D \). This exercise helps in understanding the application of trigonometric principles in physical systems involving forces and equilibrium.
Transcribed Image Text:**Title: Analysis of a System of Masses Suspended by Strings** **Figure Description and Instructions:** **Figure 2:** The diagram presents a system of four equal masses \( M \) each suspended by a string of length \( \ell \) from a horizontal support. The equal lengths of string form angles \( \theta_1 \) and \( \theta_2 \) with the vertical axis at different points in the system. **Key Components of the Diagram:** 1. **Angles with Vertical:** - At the points of attachment to the horizontal support, the strings form an angle \( \theta_1 \) with the vertical. - The strings connecting the masses form an angle \( \theta_2 \) with the vertical. 2. **String Lengths:** - The length of each suspending string from the support to the first and last mass is \( \ell \). - The lengths of strings between the masses are also \( \ell \). 3. **Overall Length:** - The total horizontal length spanned by the system of masses is denoted as \( L = 5\ell \). 4. **Horizontal Separation:** - The entire system spans a horizontal distance \( D \), which needs to be expressed in terms of \( \theta_1 \) and \( L \). **Equation to Solve:** The task is to find the total horizontal distance \( D \) in terms of the given angles \( \theta_1 \) and the total length \( L \). **Steps for Solutions:** 1. Decompose the lengths \( \ell \) into horizontal and vertical components using trigonometric functions for \( \theta_1 \) and \( \theta_2 \). 2. Sum the horizontal components to determine the overall horizontal span \( D \). 3. Apply the formula \( L = 5\ell \) to simplify and express \( D \) in terms of \( \theta_1 \) and \( L \). Given these clues and tasks, students are encouraged to use their knowledge of trigonometry to solve for \( D \). This exercise helps in understanding the application of trigonometric principles in physical systems involving forces and equilibrium.
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