**Problem Description**The magnitude of the resultant force \( F_R \) on the hook is known to be 570 N. The magnitude and direction of \( \vec{F_1} \) is unknown.**Diagram Explanation**The diagram shows three forces originating from a common point. The forces are labeled \( F_1 \), \( F_2 \), and \( F_3 \), with their respective directions shown as arrows. The resultant force \( F_R \) is also shown as an arrow. The coordinate axes are labeled \( x \) and \( y \).**Details of Forces and Angles**- \( \vec{F_1} \) is shown at an angle \( \theta_1 \) from the positive \( y \)-axis.- \( \vec{F_2} \) is aligned along the positive \( x \)-axis.- \( \vec{F_3} \) is aligned based on the dimensions provided in a 5-12-13 triangle.**Table of Known Values**| Variable | Value ||----------|-------------|| \( F_R \) | 570 N || \( \theta_2 \) | 25 degrees || \( F_2 \) | 115 N || \( F_3 \) | 265 N |**Questions**a. Find the magnitude of the unknown force \( F_1 \).b. Determine the direction of the unknown force \( F_1 \), with angle \( \theta_1 \) measured clockwise from the positive \( y \)-axis, in degrees. The answer must be between \( 0^\circ \leq \theta \leq 90^\circ \).**Instructions**Round your final answers to 3 significant digits.\( F_1 = \boxed{\phantom{000}} \)\( \theta_1 = \boxed{\phantom{000}}^\circ \) The image from wemap.org depicts a force diagram on an x-y coordinate system. It shows three forces, \( F_1 \), \( F_2 \), and \( F_3 \), and the resultant force \( F_R \).### Diagram Details:- **\( F_1 \)**: An unknown force directed upward and to the right, forming an angle \( \theta_1 \) with the positive y-axis.- **\( F_2 \)**: A known force of 115 N directed horizontally to the right along the positive x-axis.- **\( F_3 \)**: A known force of 265 N directed downward and to the left.- **\( F_R \)**: The resultant force of 570 N, directed upward and to the right, forming an angle with the positive x-axis.- **\( \theta_2 \)**: The angle of 25 degrees formed between \( F_2 \) and the x-axis.### Problem Statement:1. **Find the magnitude of the unknown force \( F_1 \)**.2. **Determine the direction of the unknown force \( F_1 \)**, measuring angle \( \theta_1 \) clockwise from the positive y-axis. The answer must be between \( 0^\circ \leq \theta \leq 90^\circ \).### Values Provided:- \( F_R = 570 \, \text{N} \)- \( \theta_2 = 25^\circ \)- \( F_2 = 115 \, \text{N} \)- \( F_3 = 265 \, \text{N} \)### Instructions:- Round the final answers to 3 significant figures:\[ F_1 = \boxed{\, \, \, \, \, \,} \, \text{N} \]\[ \theta_1 = \boxed{\, \, \, \, \, \,} \, \text{degrees} \]

Answered: Image /qna-images/answer/1fe6af32-44a2-427e-a096-0a7db50e3fd3.jpg

y 0₁ Variable FR 02 F2 F3 5 13 0₁ = 12 0₂ F3 F₁ Values for the figure are given in the following table. Note the figure may not be to scale. Value 570 N 25 degrees 115 N 265 N FR F2 a. Find the magnitude of the unknown force F₁ b. Determine the direction of the unknown force F₁, 0 measured clockwise from the positive y-axis in degrees. Answer must be between 0° ≤ 0 ≤ 90° N X Round your final answers to 3 significant digits/figures. F₁ = degrees

y 0₁ Variable FR 02 F2 F3 5 13 0₁ = 12 0₂ F3 F₁ Values for the figure are given in the following table. Note the figure may not be to scale. Value 570 N 25 degrees 115 N 265 N FR F2 a. Find the magnitude of the unknown force F₁ b. Determine the direction of the unknown force F₁, 0 measured clockwise from the positive y-axis in degrees. Answer must be between 0° ≤ 0 ≤ 90° N X Round your final answers to 3 significant digits/figures. F₁ = degrees

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Control Survey and Geodetic reductions

Control surveys or survey controls are used to establish reference points as a basis for various construction activities. Vertical and horizontal control points are to be established in a control survey to increase accuracy. After establishing the control points, all other types of surveys such as topographic, right-of-way, aerial mapping, construction layout, boundary surveys, and utility mapping can be worked upon so that control networks can be formed. The place from which the observations are made is called a survey station.

Question

**Problem Description**

The magnitude of the resultant force \( F_R \) on the hook is known to be 570 N. The magnitude and direction of \( \vec{F_1} \) is unknown.

**Diagram Explanation**

The diagram shows three forces originating from a common point. The forces are labeled \( F_1 \), \( F_2 \), and \( F_3 \), with their respective directions shown as arrows. The resultant force \( F_R \) is also shown as an arrow. The coordinate axes are labeled \( x \) and \( y \).

**Details of Forces and Angles**

- \( \vec{F_1} \) is shown at an angle \( \theta_1 \) from the positive \( y \)-axis.
- \( \vec{F_2} \) is aligned along the positive \( x \)-axis.
- \( \vec{F_3} \) is aligned based on the dimensions provided in a 5-12-13 triangle.

**Table of Known Values**

| Variable | Value |
|----------|-------------|
| \( F_R \) | 570 N |
| \( \theta_2 \) | 25 degrees |
| \( F_2 \) | 115 N |
| \( F_3 \) | 265 N |

**Questions**

a. Find the magnitude of the unknown force \( F_1 \).

b. Determine the direction of the unknown force \( F_1 \), with angle \( \theta_1 \) measured clockwise from the positive \( y \)-axis, in degrees. The answer must be between \( 0^\circ \leq \theta \leq 90^\circ \).

**Instructions**

Round your final answers to 3 significant digits.

\( F_1 = \boxed{\phantom{000}} \)

\( \theta_1 = \boxed{\phantom{000}}^\circ \)

The image from wemap.org depicts a force diagram on an x-y coordinate system. It shows three forces, \( F_1 \), \( F_2 \), and \( F_3 \), and the resultant force \( F_R \).

### Diagram Details:

- **\( F_1 \)**: An unknown force directed upward and to the right, forming an angle \( \theta_1 \) with the positive y-axis.
- **\( F_2 \)**: A known force of 115 N directed horizontally to the right along the positive x-axis.
- **\( F_3 \)**: A known force of 265 N directed downward and to the left.
- **\( F_R \)**: The resultant force of 570 N, directed upward and to the right, forming an angle with the positive x-axis.
- **\( \theta_2 \)**: The angle of 25 degrees formed between \( F_2 \) and the x-axis.

### Problem Statement:

1. **Find the magnitude of the unknown force \( F_1 \)**.
2. **Determine the direction of the unknown force \( F_1 \)**, measuring angle \( \theta_1 \) clockwise from the positive y-axis. The answer must be between \( 0^\circ \leq \theta \leq 90^\circ \).

### Values Provided:

- \( F_R = 570 \, \text{N} \)
- \( \theta_2 = 25^\circ \)
- \( F_2 = 115 \, \text{N} \)
- \( F_3 = 265 \, \text{N} \)

### Instructions:

- Round the final answers to 3 significant figures:

\[ F_1 = \boxed{\, \, \, \, \, \,} \, \text{N} \]

\[ \theta_1 = \boxed{\, \, \, \, \, \,} \, \text{degrees} \]

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