Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter11: Angular Momentum
Section: Chapter Questions
Problem 11.3OQ: Let us name three perpendicular directions as right, up, and toward you as you might name them when...
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How do you solve for Resultant given this information. I was able to do the graphical method but I am unsure how n how to use the component method.
![### Vector Addition
**Given Vectors:**
- \( F_1 = 1.47 \, \text{units} \) at \( 0^\circ \)
- \( F_2 = 1.96 \, \text{units} \) at \( 90^\circ \)
**Graph Explanation:**
The provided graph is a Cartesian coordinate system with labeled axes, representing a vector addition problem.
**Vectors on the Graph:**
1. **Vector \( F_1 \) (Blue Arrow)**
- Magnitude: 1.47 units
- Direction: \( 0^\circ \) (positive x-axis)
- Plotted from the origin (0,0) to the point (1.47, 0)
2. **Vector \( F_2 \) (Blue Arrow)**
- Magnitude: 1.96 units
- Direction: \( 90^\circ \) (positive y-axis)
- Plotted from the origin (0,0) to the point (0, 1.96)
**Resultant Vector \( F_r \) (Black Arrow and Dotted Lines)**
- The resultant vector \( F_r \) starts from the origin and ends at the point where the two original vectors combine, forming the hypotenuse of the right triangle created by \( F_1 \) and \( F_2 \).
- Magnitude: Approximately 1.9 units
- Direction: \( 45^\circ \)
**Forming the Resultant Vector:**
The resultant vector \( F_r \) can be found by placing the tail of \( F_2 \) at the head of \( F_1 \). This forms a right triangle with:
- The horizontal component as \( F_1 \)
- The vertical component as \( F_2 \)
In accordance with the Pythagorean theorem, the magnitude of \( F_r \) is calculated as:
\[ F_r = \sqrt{F_1^2 + F_2^2} \]
\[ F_r = \sqrt{1.47^2 + 1.96^2} \approx 2.45 \text{ units} \]
**Conclusion:**
The graph visually demonstrates the vector addition process, with the components \( F_1 \) and \( F_2 \) and their resultant vector \( F_r \). This graphical method helps](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb72c24d2-e42d-4897-97a3-bd7ae212f23e%2Fb90e2c11-bb67-4b23-88c0-4aecd68ed083%2F1tvb63_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Vector Addition
**Given Vectors:**
- \( F_1 = 1.47 \, \text{units} \) at \( 0^\circ \)
- \( F_2 = 1.96 \, \text{units} \) at \( 90^\circ \)
**Graph Explanation:**
The provided graph is a Cartesian coordinate system with labeled axes, representing a vector addition problem.
**Vectors on the Graph:**
1. **Vector \( F_1 \) (Blue Arrow)**
- Magnitude: 1.47 units
- Direction: \( 0^\circ \) (positive x-axis)
- Plotted from the origin (0,0) to the point (1.47, 0)
2. **Vector \( F_2 \) (Blue Arrow)**
- Magnitude: 1.96 units
- Direction: \( 90^\circ \) (positive y-axis)
- Plotted from the origin (0,0) to the point (0, 1.96)
**Resultant Vector \( F_r \) (Black Arrow and Dotted Lines)**
- The resultant vector \( F_r \) starts from the origin and ends at the point where the two original vectors combine, forming the hypotenuse of the right triangle created by \( F_1 \) and \( F_2 \).
- Magnitude: Approximately 1.9 units
- Direction: \( 45^\circ \)
**Forming the Resultant Vector:**
The resultant vector \( F_r \) can be found by placing the tail of \( F_2 \) at the head of \( F_1 \). This forms a right triangle with:
- The horizontal component as \( F_1 \)
- The vertical component as \( F_2 \)
In accordance with the Pythagorean theorem, the magnitude of \( F_r \) is calculated as:
\[ F_r = \sqrt{F_1^2 + F_2^2} \]
\[ F_r = \sqrt{1.47^2 + 1.96^2} \approx 2.45 \text{ units} \]
**Conclusion:**
The graph visually demonstrates the vector addition process, with the components \( F_1 \) and \( F_2 \) and their resultant vector \( F_r \). This graphical method helps
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