**Problem Statement:**Find the magnitude of the tension (in N) in each supporting cable shown below. In each case, the weight of the suspended body is 170.0 N and the masses of the cables are negligible. (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)**Diagrams and Explanation:**(a) **Diagram (a)**:- A suspended body is hanging from a system of three cables.- The cables are labeled as \( T_1 \), \( T_2 \), and \( T_3 \).- \( T_1 \) is at a 45° angle to the horizontal.- \( T_3 \) is vertical.- There are input boxes for entering the tension values in Newtons for \( T_1 \), \( T_2 \), and \( T_3 \).\[ T_1 = \_\_\_\_ \, \text{N} \]\[ T_2 = \_\_\_\_ \, \text{N} \]\[ T_3 = \_\_\_\_ \, \text{N} \](b) **Diagram (b)**:- A suspended body is hanging from a system of two cables.- The cables are labeled as \( T_1 \) and \( T_2 \).- Both cables make an angle of 60° with the horizontal.- There are input boxes for entering the tension values in Newtons for \( T_1 \) and \( T_2 \).\[ T_1 = \_\_\_\_ \, \text{N} \]\[ T_2 = \_\_\_\_ \, \text{N} \]**Instructions:**- Use accurate calculations without rounding intermediate values to determine the tensions in the cables.- The tensions need to satisfy the equilibrium conditions for the forces in both the horizontal and vertical directions. The image includes two diagrams labeled (c) and (d), illustrating systems of connected ropes and masses.**Diagram (c):**- A mass is suspended by three ropes. - Two ropes (labeled \( T_1 \) and \( T_2 \)) are attached to a fixed support at angles of 60° and 45° respectively relative to the horizontal. These angles are labeled on the image.- A third rope \( T_3 \) hangs vertically downward, attaching to a mass at the bottom.- Below the diagram, there are three boxes where the tension in each rope (\( T_1 \), \( T_2 \), and \( T_3 \)) can be calculated and entered, with the unit of Newtons (N).**Diagram (d):**- A system with four ropes, where a mass is suspended at the bottom.- Ropes \( T_1 \) and \( T_2 \) are attached to the fixed support at angles of 45° each from the horizontal.- Ropes \( T_3 \) and \( T_4 \) are positioned vertically below, with \( T_3 \) at a 60° angle converging toward \( T_4 \), which is vertical.- There are four boxes for inputting the calculated tensions in ropes (\( T_1 \), \( T_2 \), \( T_3 \), and \( T_4 \)), all measured in Newtons (N).These diagrams are used to analyze static equilibrium conditions where the tensions in the ropes balance out the gravitational force on the hanging mass.

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Find the magnitude of the tension (in N) in each supporting cable shown below. In each case, the weight of the suspended body is 170.0 N and the masses of the cables are negligible. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) (a) 45° T2 T3 T1 T2 = N N (b) 60° 60° T2 T = T, =

Find the magnitude of the tension (in N) in each supporting cable shown below. In each case, the weight of the suspended body is 170.0 N and the masses of the cables are negligible. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) (a) 45° T2 T3 T1 T2 = N N (b) 60° 60° T2 T = T, =

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Rotational Equilibrium And Rotational Dynamics

In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.

Equilibrium of Forces

The tension created on one body during push or pull is known as force.

Question

**Problem Statement:**

Find the magnitude of the tension (in N) in each supporting cable shown below. In each case, the weight of the suspended body is 170.0 N and the masses of the cables are negligible. (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)

**Diagrams and Explanation:**

(a) **Diagram (a)**:
- A suspended body is hanging from a system of three cables.
- The cables are labeled as \( T_1 \), \( T_2 \), and \( T_3 \).
- \( T_1 \) is at a 45° angle to the horizontal.
- \( T_3 \) is vertical.
- There are input boxes for entering the tension values in Newtons for \( T_1 \), \( T_2 \), and \( T_3 \).

\[ T_1 = \_\_\_\_ \, \text{N} \]

\[ T_2 = \_\_\_\_ \, \text{N} \]

\[ T_3 = \_\_\_\_ \, \text{N} \]

(b) **Diagram (b)**:
- A suspended body is hanging from a system of two cables.
- The cables are labeled as \( T_1 \) and \( T_2 \).
- Both cables make an angle of 60° with the horizontal.
- There are input boxes for entering the tension values in Newtons for \( T_1 \) and \( T_2 \).

\[ T_1 = \_\_\_\_ \, \text{N} \]

\[ T_2 = \_\_\_\_ \, \text{N} \]

**Instructions:**
- Use accurate calculations without rounding intermediate values to determine the tensions in the cables.
- The tensions need to satisfy the equilibrium conditions for the forces in both the horizontal and vertical directions.

The image includes two diagrams labeled (c) and (d), illustrating systems of connected ropes and masses.

**Diagram (c):**
- A mass is suspended by three ropes.
- Two ropes (labeled \( T_1 \) and \( T_2 \)) are attached to a fixed support at angles of 60° and 45° respectively relative to the horizontal. These angles are labeled on the image.
- A third rope \( T_3 \) hangs vertically downward, attaching to a mass at the bottom.
- Below the diagram, there are three boxes where the tension in each rope (\( T_1 \), \( T_2 \), and \( T_3 \)) can be calculated and entered, with the unit of Newtons (N).

**Diagram (d):**
- A system with four ropes, where a mass is suspended at the bottom.
- Ropes \( T_1 \) and \( T_2 \) are attached to the fixed support at angles of 45° each from the horizontal.
- Ropes \( T_3 \) and \( T_4 \) are positioned vertically below, with \( T_3 \) at a 60° angle converging toward \( T_4 \), which is vertical.
- There are four boxes for inputting the calculated tensions in ropes (\( T_1 \), \( T_2 \), \( T_3 \), and \( T_4 \)), all measured in Newtons (N).

These diagrams are used to analyze static equilibrium conditions where the tensions in the ropes balance out the gravitational force on the hanging mass.

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