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2. Using Tip to Tail or the Parallelogram method, calculate the resultant force. 30° Q = 45 N 15° Figure 2. P = 35 N

2. Using Tip to Tail or the Parallelogram method, calculate the resultant force. 30° Q = 45 N 15° Figure 2. P = 35 N

Structural Analysis
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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**Figure 2 Explanation for Educational Website** The diagram illustrates a vector composition problem. The task is to calculate the resultant force using either the Tip to Tail method or the Parallelogram method. **Vectors:** - Vector \( Q \) has a magnitude of \( 45 \, \text{N} \) and is represented by a blue arrow pointing upwards at an angle of \( 30^\circ \) from the horizontal axis. - Vector \( P \) has a magnitude of \( 35 \, \text{N} \) and is represented by a red arrow pointing rightward at an angle of \( 15^\circ \) from the horizontal axis. **Description:** 1. **Vector Orientation:** - The origin is marked by a purple dot where both vectors begin. - Vector \( P \) makes an angle of \( 15^\circ \) with the horizontal axis, indicating its slight upward tilt. - Vector \( Q \) is oriented at a \( 30^\circ \) angle from the horizontal axis, pointing upwards. 2. **Angle Measurement:** - The angles are measured from the horizontal axis to the respective vectors. - These angles are important for applying trigonometric principles in calculating the resultant force. **Methods for Calculating Resultant Force:** - **Tip to Tail Method:** Position the tail of vector \( Q \) at the tip of vector \( P \), then draw the resultant vector from the tail of \( P \) to the tip of \( Q \). - **Parallelogram Method:** Construct a parallelogram using vectors \( P \) and \( Q \) as adjacent sides. The diagonal of the parallelogram represents the resultant vector. Understanding and applying these vector composition techniques is essential for determining the magnitude and direction of the resultant force accurately.
Transcribed Image Text:**Figure 2 Explanation for Educational Website** The diagram illustrates a vector composition problem. The task is to calculate the resultant force using either the Tip to Tail method or the Parallelogram method. **Vectors:** - Vector \( Q \) has a magnitude of \( 45 \, \text{N} \) and is represented by a blue arrow pointing upwards at an angle of \( 30^\circ \) from the horizontal axis. - Vector \( P \) has a magnitude of \( 35 \, \text{N} \) and is represented by a red arrow pointing rightward at an angle of \( 15^\circ \) from the horizontal axis. **Description:** 1. **Vector Orientation:** - The origin is marked by a purple dot where both vectors begin. - Vector \( P \) makes an angle of \( 15^\circ \) with the horizontal axis, indicating its slight upward tilt. - Vector \( Q \) is oriented at a \( 30^\circ \) angle from the horizontal axis, pointing upwards. 2. **Angle Measurement:** - The angles are measured from the horizontal axis to the respective vectors. - These angles are important for applying trigonometric principles in calculating the resultant force. **Methods for Calculating Resultant Force:** - **Tip to Tail Method:** Position the tail of vector \( Q \) at the tip of vector \( P \), then draw the resultant vector from the tail of \( P \) to the tip of \( Q \). - **Parallelogram Method:** Construct a parallelogram using vectors \( P \) and \( Q \) as adjacent sides. The diagonal of the parallelogram represents the resultant vector. Understanding and applying these vector composition techniques is essential for determining the magnitude and direction of the resultant force accurately.
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