2/1 The force F has a magnitude of 600 N. Express F as a vector in terms of the unit vectors i and j. Identify the x and y scalar components of F. 40° F = 600 N PROBLEM 2/1
2/1 The force F has a magnitude of 600 N. Express F as a vector in terms of the unit vectors i and j. Identify the x and y scalar components of F. 40° F = 600 N PROBLEM 2/1
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
please show all details
![**Problem 2/1:**
The force **F** has a magnitude of 600 N. Express **F** as a vector in terms of the unit vectors **i** and **j**. Identify the **x** and **y** scalar components of **F**.
**Diagram Details:**
The diagram is a Cartesian coordinate system with the origin labeled **O**. The **x** and **y** axes are shown as dashed lines intersecting at the origin. A vector representing the force **F** is drawn from the origin, making a 40° angle with the negative **x** axis. The vector **F** is labeled as having a magnitude of 600 N, pointing towards the third quadrant of the coordinate plane.
**Solution:**
To find the **x** and **y** components of **F**, we can use trigonometric functions based on the given angle (40°) and the magnitude of the vector (600 N).
1. **x-component**:
\[ F_x = |F| \cos(\theta) \]
\[ F_x = 600 \cos(40°) \]
\[ F_x \approx 600 \times 0.766 \approx 459.6 \, \text{N} \]
Since the force is in the third quadrant, the **x**-component will be negative:
\[ F_x \approx -459.6 \, \text{N} \]
2. **y-component**:
\[ F_y = |F| \sin(\theta) \]
\[ F_y = 600 \sin(40°) \]
\[ F_y \approx 600 \times 0.643 \approx 385.8 \, \text{N} \]
Similarly, since the force is in the third quadrant, the **y**-component will be negative:
\[ F_y \approx -385.8 \, \text{N} \]
Therefore, the vector **F** in terms of the unit vectors **i** and **j** can be written as:
\[ \mathbf{F} = -459.6 \mathbf{i} - 385.8 \mathbf{j} \]
**Summary:**
- **x-component of F:** \[ -459.6 \, \text{N} \]
- **y-component of F:** \[ -385.8 \, \text{N} \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf950827-7d70-472f-a52e-1d3c26fa2196%2Fc5dfdce7-a72f-4fbf-9679-9f1a75b52756%2F54cs07s_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2/1:**
The force **F** has a magnitude of 600 N. Express **F** as a vector in terms of the unit vectors **i** and **j**. Identify the **x** and **y** scalar components of **F**.
**Diagram Details:**
The diagram is a Cartesian coordinate system with the origin labeled **O**. The **x** and **y** axes are shown as dashed lines intersecting at the origin. A vector representing the force **F** is drawn from the origin, making a 40° angle with the negative **x** axis. The vector **F** is labeled as having a magnitude of 600 N, pointing towards the third quadrant of the coordinate plane.
**Solution:**
To find the **x** and **y** components of **F**, we can use trigonometric functions based on the given angle (40°) and the magnitude of the vector (600 N).
1. **x-component**:
\[ F_x = |F| \cos(\theta) \]
\[ F_x = 600 \cos(40°) \]
\[ F_x \approx 600 \times 0.766 \approx 459.6 \, \text{N} \]
Since the force is in the third quadrant, the **x**-component will be negative:
\[ F_x \approx -459.6 \, \text{N} \]
2. **y-component**:
\[ F_y = |F| \sin(\theta) \]
\[ F_y = 600 \sin(40°) \]
\[ F_y \approx 600 \times 0.643 \approx 385.8 \, \text{N} \]
Similarly, since the force is in the third quadrant, the **y**-component will be negative:
\[ F_y \approx -385.8 \, \text{N} \]
Therefore, the vector **F** in terms of the unit vectors **i** and **j** can be written as:
\[ \mathbf{F} = -459.6 \mathbf{i} - 385.8 \mathbf{j} \]
**Summary:**
- **x-component of F:** \[ -459.6 \, \text{N} \]
- **y-component of F:** \[ -385.8 \, \text{N} \
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you


Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning


Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning

Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education


Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning