### Problem Statement#### A)If the equivalent single force of the system is 300 kN acting up along the y-axis, determine the magnitude and direction of \( F_2 \) and its direction if \( F_3 = 251 \, \text{N} \) and \( F = 416.55 \, \text{N} \) and \( \alpha = 65^\circ \).#### B)If the equivalent single force of the system is zero, determine the magnitude and direction of \( F \), and its direction if \( F_3 = 456 \, \text{N} \) and \( F_2 = 260 \, \text{N} \) and \( \beta = 35^\circ \).#### C)If the equivalent single force of the system is \( 200 \mathbf{i} - 160 \mathbf{j} \), determine the magnitude and direction of \( F_2 \) and its direction if \( F_3 = 355 \, \text{N} \) and \( F_1 = 285 \, \text{N} \) and \( \alpha = 30^\circ \).### Diagram ExplanationThe diagram on the right consists of vectors labeled \( F_1 \), \( F_2 \), and \( F_3 \), each represented by arrows originating from a common origin. - \( F_1 \) is along the positive y-axis.- \( F_2 \) is at an angle \( \beta \) from the x-axis.- \( F_3 \) is along the negative x-axis.- The angle \( \alpha \) is between \( F_1 \) and the line parallel to the x-axis. ### Instructions1. Use vector addition to resolve the forces into components.2. Apply trigonometric functions to determine the angles given the magnitudes and directions.3. Solve the equations to find unknown magnitudes and directions for each problem part.

Given data in question Resultant = 300 kN Angles Forces To find out Values of forces and angle

A) IF THE EQUIVALENT SINGLE FORCE Or THE SYSTEM IS 300 KN ACTING Ur ALONG THE Y-AXIS, DETERMINE THE MAGN ITUDE AND DIRECTION OF F2 AND 73 DIRECTION IT F3: 251 N AND F=416.55 N AND a l65. FI IF THE EQUIVA LE NT SINGLE FORCE OF THE SYSTEM IS ERO +3 a THE MAGNITUDE AND DIRECTON or F, AND IT3 DIRECTION IF F3 456 N AND 12 260N ANO BE 35 DETERMINE c) IF THE EQUIVA LENT SINGLE FORCE OF TTE SVSTEM IS 2001- /60j, DETERM INE THE MAGNTUDE AND DIRECTION OF F2 AND ITS DIRECTION IF F3: 355N AND FI-285N AND a 30.

A) IF THE EQUIVALENT SINGLE FORCE Or THE SYSTEM IS 300 KN ACTING Ur ALONG THE Y-AXIS, DETERMINE THE MAGN ITUDE AND DIRECTION OF F2 AND 73 DIRECTION IT F3: 251 N AND F=416.55 N AND a l65. FI IF THE EQUIVA LE NT SINGLE FORCE OF THE SYSTEM IS ERO +3 a THE MAGNITUDE AND DIRECTON or F, AND IT3 DIRECTION IF F3 456 N AND 12 260N ANO BE 35 DETERMINE c) IF THE EQUIVA LENT SINGLE FORCE OF TTE SVSTEM IS 2001- /60j, DETERM INE THE MAGNTUDE AND DIRECTION OF F2 AND ITS DIRECTION IF F3: 355N AND FI-285N AND a 30.

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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Question

### Problem Statement

#### A)
If the equivalent single force of the system is 300 kN acting up along the y-axis, determine the magnitude and direction of \( F_2 \) and its direction if \( F_3 = 251 \, \text{N} \) and \( F = 416.55 \, \text{N} \) and \( \alpha = 65^\circ \).

#### B)
If the equivalent single force of the system is zero, determine the magnitude and direction of \( F \), and its direction if \( F_3 = 456 \, \text{N} \) and \( F_2 = 260 \, \text{N} \) and \( \beta = 35^\circ \).

#### C)
If the equivalent single force of the system is \( 200 \mathbf{i} - 160 \mathbf{j} \), determine the magnitude and direction of \( F_2 \) and its direction if \( F_3 = 355 \, \text{N} \) and \( F_1 = 285 \, \text{N} \) and \( \alpha = 30^\circ \).

### Diagram Explanation

The diagram on the right consists of vectors labeled \( F_1 \), \( F_2 \), and \( F_3 \), each represented by arrows originating from a common origin.

- \( F_1 \) is along the positive y-axis.
- \( F_2 \) is at an angle \( \beta \) from the x-axis.
- \( F_3 \) is along the negative x-axis.
- The angle \( \alpha \) is between \( F_1 \) and the line parallel to the x-axis.

### Instructions

1. Use vector addition to resolve the forces into components.
2. Apply trigonometric functions to determine the angles given the magnitudes and directions.
3. Solve the equations to find unknown magnitudes and directions for each problem part.

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