College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question
![**Problem Statement:**
What is the **direction** of the net force (F = F₁ + F₂), measured in degrees in CCW direction from the +x axis?
---
**Explanation with Diagram:**
In the image provided, we see an illustration of two forces acting in the plane. The forces are represented as vectors, and their magnitudes and directions are explicitly given. Here is a detailed explanation of the components:
- **F₁ = 30N**: This vector is directed at an angle of 30° above the positive x-axis.
- **F₂ = 18N**: This vector is directed at an angle of 50° above the negative x-axis.
The diagram features a standard x (horizontal) and y (vertical) coordinate system:
- The origin is at the intersection of the x and y axes.
- The positive x-axis points towards the right.
- The positive y-axis points upwards.
Vector **F₁** is drawn at a 30° angle counterclockwise (CCW) from the positive x-axis, and vector **F₂** is drawn at a 50° angle clockwise from the negative x-axis. The task is to determine the direction of the net resultant vector F = F₁ + F₂ in degrees, measured CCW from the positive x-axis.
The general strategy to solve this involves:
1. Resolving each force vector into its respective x and y components.
2. Summing these components to find the resultant vector's components.
3. Using trigonometry to find the angle of the resultant vector relative to the positive x-axis.
**Diagram Explanation:**
The diagram visually demonstrates the given forces:
```
y
|
| F₁ = 30N
| /
| /
| / 30°
| /
|
|
F₂ = 18N```
50°
--------- x
```
**Note:** The resultant angle can be determined using vector resolution and trigonometric calculations.
By following these steps, students can determine the direction of the net force vector.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcde4937d-e883-446c-8941-8d2ade4d99b0%2Facd7faf9-5aff-47ae-9871-ea1bcbe5d8d4%2Fmq2m9li_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
What is the **direction** of the net force (F = F₁ + F₂), measured in degrees in CCW direction from the +x axis?
---
**Explanation with Diagram:**
In the image provided, we see an illustration of two forces acting in the plane. The forces are represented as vectors, and their magnitudes and directions are explicitly given. Here is a detailed explanation of the components:
- **F₁ = 30N**: This vector is directed at an angle of 30° above the positive x-axis.
- **F₂ = 18N**: This vector is directed at an angle of 50° above the negative x-axis.
The diagram features a standard x (horizontal) and y (vertical) coordinate system:
- The origin is at the intersection of the x and y axes.
- The positive x-axis points towards the right.
- The positive y-axis points upwards.
Vector **F₁** is drawn at a 30° angle counterclockwise (CCW) from the positive x-axis, and vector **F₂** is drawn at a 50° angle clockwise from the negative x-axis. The task is to determine the direction of the net resultant vector F = F₁ + F₂ in degrees, measured CCW from the positive x-axis.
The general strategy to solve this involves:
1. Resolving each force vector into its respective x and y components.
2. Summing these components to find the resultant vector's components.
3. Using trigonometry to find the angle of the resultant vector relative to the positive x-axis.
**Diagram Explanation:**
The diagram visually demonstrates the given forces:
```
y
|
| F₁ = 30N
| /
| /
| / 30°
| /
|
|
F₂ = 18N```
50°
--------- x
```
**Note:** The resultant angle can be determined using vector resolution and trigonometric calculations.
By following these steps, students can determine the direction of the net force vector.
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