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A. Draw a different configuration, and make it a diagram similar to Fig. 3. Specify each mass and angle you’d be using. B. Determine the tensions T1 and T2 which would be created by each hanging mass C. find the unknown components of T3 D.calculate the magnitude and direction of T3

A. Draw a different configuration, and make it a diagram similar to Fig. 3. Specify each mass and angle you’d be using. B. Determine the tensions T1 and T2 which would be created by each hanging mass C. find the unknown components of T3 D.calculate the magnitude and direction of T3

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. Draw a different configuration, and make it a diagram similar to Fig. 3. Specify
each mass and angle you’d be using.
B. Determine the tensions T1 and T2 which would be created by each hanging
mass
C. find the unknown components of T3
D.calculate the magnitude and direction of T3

**1 Background** Forces are pushes and pulls. When you hang a mass from a string, the mass feels a force called **weight** (\(w\)) that pulls it down, and an equal force called **tension** (\(T\)) that pulls up on it. When the weight and tension are equal, the mass is in **equilibrium**. You can determine the weight of a mass by first converting its mass into kilograms and then multiplying by the acceleration of gravity: \[ w = mg \quad (1) \] For each hanging mass in this experiment, the tension in its string will be equal to its weight. The experimental setup would look something like the sketch in Fig. 1. *Figure 1: A sketch of a force table with two hanging masses creating two tensions on a ring in the center.* The top down view will look something like Fig 2. *Figure 2: A circle divided into four quadrants depicting angles 0°, 90°, 180°, and 270°. It illustrates two tension forces, \(T_1\) and \(T_2\), acting at different angles on a central point.* If you were to let these masses go, they would fall! We need a third force to balance them, and that force will have to have some magnitude \(T_3\) at some angle \(\theta_3\). Adding the third force in makes the diagram look like Fig 3.
Transcribed Image Text:**1 Background** Forces are pushes and pulls. When you hang a mass from a string, the mass feels a force called **weight** (\(w\)) that pulls it down, and an equal force called **tension** (\(T\)) that pulls up on it. When the weight and tension are equal, the mass is in **equilibrium**. You can determine the weight of a mass by first converting its mass into kilograms and then multiplying by the acceleration of gravity: \[ w = mg \quad (1) \] For each hanging mass in this experiment, the tension in its string will be equal to its weight. The experimental setup would look something like the sketch in Fig. 1. *Figure 1: A sketch of a force table with two hanging masses creating two tensions on a ring in the center.* The top down view will look something like Fig 2. *Figure 2: A circle divided into four quadrants depicting angles 0°, 90°, 180°, and 270°. It illustrates two tension forces, \(T_1\) and \(T_2\), acting at different angles on a central point.* If you were to let these masses go, they would fall! We need a third force to balance them, and that force will have to have some magnitude \(T_3\) at some angle \(\theta_3\). Adding the third force in makes the diagram look like Fig 3.
The diagram depicts a circle with three forces, \( \vec{T}_1 \), \( \vec{T}_2 \), and \( \vec{T}_3 \), acting at angles of 0°, 90°, and 180° respectively. Each force is represented by an arrow pointing outward from the center of the circle, illustrating their directions. **Figure 3: Three forces that balance each other** Below the figure, the text discusses forces in equilibrium, noting the equation that describes this state: \[ \vec{T}_1 + \vec{T}_2 + \vec{T}_3 = 0 \quad (2) \] The discussion follows by suggesting that while the vectors can be added graphically, obtaining precise values is simpler through algebraic addition. This involves resolving each vector into its x and y components as shown: \[ \vec{T}_{1x} + \vec{T}_{2x} + \vec{T}_{3x} = 0 \quad (3) \] \[ \vec{T}_{1y} + \vec{T}_{2y} + \vec{T}_{3y} = 0 \quad (4) \]
Transcribed Image Text:The diagram depicts a circle with three forces, \( \vec{T}_1 \), \( \vec{T}_2 \), and \( \vec{T}_3 \), acting at angles of 0°, 90°, and 180° respectively. Each force is represented by an arrow pointing outward from the center of the circle, illustrating their directions. **Figure 3: Three forces that balance each other** Below the figure, the text discusses forces in equilibrium, noting the equation that describes this state: \[ \vec{T}_1 + \vec{T}_2 + \vec{T}_3 = 0 \quad (2) \] The discussion follows by suggesting that while the vectors can be added graphically, obtaining precise values is simpler through algebraic addition. This involves resolving each vector into its x and y components as shown: \[ \vec{T}_{1x} + \vec{T}_{2x} + \vec{T}_{3x} = 0 \quad (3) \] \[ \vec{T}_{1y} + \vec{T}_{2y} + \vec{T}_{3y} = 0 \quad (4) \]
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