What is the direction of the net Force (F= F₁+F₂), measured in degrees in CCW direction from the +x axis? F₂=18N 50 y 30° F=30N x

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Chapter1: Units, Trigonometry. And Vectors
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**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.
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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