A Freebody diagram is foreign object is shown in the figure. FA = 420 N, FB = 300 N, FC = 275N, and FD = 295N. Assume angle left = 31degrees, and alpha =13 degree. How much work in (J) does FA do on the object if it moves 2.9 m downward?

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Chapter1: Units, Trigonometry. And Vectors
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Will rate!! A Freebody diagram is foreign object is shown in the figure. FA = 420 N, FB = 300 N, FC = 275N, and FD = 295N. Assume angle left = 31degrees, and alpha =13 degree. How much work in (J) does FA do on the object if it moves 2.9 m downward?
### 3D Vector Representation with Spherical Coordinates

The image presents a three-dimensional vector diagram, which is commonly used in physics and mathematics to represent vectors in space with spherical coordinates. The diagram consists of four vectors originating from a common point, indicated by a blue circle. These vectors are labeled A, B, C, and D, distinguished using different colors for clarity:

- **Vector A** – Red
- **Vector B** – Green
- **Vector C** – Purple
- **Vector D** – Black

Two angles are marked to define the orientation of these vectors:

1. **Angle φ (phi)**: This angle lies in the horizontal plane and is measured from the positive x-axis (C) to the projection of vector A on this plane. In this diagram, it is the angle between the red vector (A) and the dashed horizontal reference line.

2. **Angle α (alpha)**: This angle is measured between the projection of vector B (green) onto the horizontal plane and the vector itself (B). It represents the elevation angle from the horizontal plane to the vector.

### Description of Vectors:
- **Vector A** (Red): It is oriented upwards and to the left at an angle φ relative to the dashed horizontal line.
- **Vector B** (Green): It is oriented upwards and to the right forming an angle α with Vector C (Purple).
- **Vector C** (Purple): This vector lies horizontally to the right.
- **Vector D** (Black): This vector points directly downward.

### Concepts Illustrated:
- **Vector Components**: This diagram helps in visualizing how a vector can be broken down into its components along different axes.
- **Spherical Coordinates**: The angles α and φ are used to describe the vector's orientation in 3D space, essential in converting between Cartesian and spherical coordinate systems.

This representation is essential for understanding various physical phenomena, such as forces, electric and magnetic fields, and the movement of objects in space.
Transcribed Image Text:### 3D Vector Representation with Spherical Coordinates The image presents a three-dimensional vector diagram, which is commonly used in physics and mathematics to represent vectors in space with spherical coordinates. The diagram consists of four vectors originating from a common point, indicated by a blue circle. These vectors are labeled A, B, C, and D, distinguished using different colors for clarity: - **Vector A** – Red - **Vector B** – Green - **Vector C** – Purple - **Vector D** – Black Two angles are marked to define the orientation of these vectors: 1. **Angle φ (phi)**: This angle lies in the horizontal plane and is measured from the positive x-axis (C) to the projection of vector A on this plane. In this diagram, it is the angle between the red vector (A) and the dashed horizontal reference line. 2. **Angle α (alpha)**: This angle is measured between the projection of vector B (green) onto the horizontal plane and the vector itself (B). It represents the elevation angle from the horizontal plane to the vector. ### Description of Vectors: - **Vector A** (Red): It is oriented upwards and to the left at an angle φ relative to the dashed horizontal line. - **Vector B** (Green): It is oriented upwards and to the right forming an angle α with Vector C (Purple). - **Vector C** (Purple): This vector lies horizontally to the right. - **Vector D** (Black): This vector points directly downward. ### Concepts Illustrated: - **Vector Components**: This diagram helps in visualizing how a vector can be broken down into its components along different axes. - **Spherical Coordinates**: The angles α and φ are used to describe the vector's orientation in 3D space, essential in converting between Cartesian and spherical coordinate systems. This representation is essential for understanding various physical phenomena, such as forces, electric and magnetic fields, and the movement of objects in space.
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