A. Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC B. Determine the y coordinate of each coin described in Part A: yA, yB, and yC. C. Determine the x and y coordinates xcg and ycg of the center of gravity of the three coins described in Part A.

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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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A. Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC

B. Determine the y coordinate of each coin described in Part A: yA, yB, and yC.

C. Determine the x and y coordinates xcg and ycg of the center of gravity of the three coins described in Part A.

The image presents a diagram with three labeled points: A, B, and C. These points are connected by lines forming an L-shape, each representing positions on an x-y coordinate plane.

**Description of Points:**
- **Point A** is located at the coordinates (0, 10.0 cm) on the y-axis.
- **Point B** is positioned at the origin with coordinates (0, 0).
- **Point C** is situated at the coordinates (10.0 cm, 0) on the x-axis.

**Axes:**
- The x-axis is labeled with the unit "cm" and extends horizontally.
- The y-axis is similarly labeled "cm" and extends vertically.

The lines connecting the points indicate that:
- There is a vertical line from Point B to Point A.
- There is a horizontal line from Point B to Point C.

The diagram effectively illustrates a right-angled arrangement between the three points, showcasing their respective distances along the x and y coordinates in centimeters.
Transcribed Image Text:The image presents a diagram with three labeled points: A, B, and C. These points are connected by lines forming an L-shape, each representing positions on an x-y coordinate plane. **Description of Points:** - **Point A** is located at the coordinates (0, 10.0 cm) on the y-axis. - **Point B** is positioned at the origin with coordinates (0, 0). - **Point C** is situated at the coordinates (10.0 cm, 0) on the x-axis. **Axes:** - The x-axis is labeled with the unit "cm" and extends horizontally. - The y-axis is similarly labeled "cm" and extends vertically. The lines connecting the points indicate that: - There is a vertical line from Point B to Point A. - There is a horizontal line from Point B to Point C. The diagram effectively illustrates a right-angled arrangement between the three points, showcasing their respective distances along the x and y coordinates in centimeters.
**Tactics Box 7.1: Finding the Center of Gravity**

1. **Choose an origin for your coordinate system.** You can choose any convenient point as the origin.

2. **Determine the coordinates \((x_1, y_1), (x_2, y_2), (x_3, y_3), \ldots\)** for the particles of mass \(m_1, m_2, m_3, \ldots\), respectively.

3. **The \(x\) coordinate of the center of gravity is**

   \[
   x_{cg} = \frac{x_1 m_1 + x_2 m_2 + x_3 m_3 + \cdots}{m_1 + m_2 + m_3 + \cdots}
   \]

4. **Similarly, the \(y\) coordinate of the center of gravity is**

   \[
   y_{cg} = \frac{y_1 m_1 + y_2 m_2 + y_3 m_3 + \cdots}{m_1 + m_2 + m_3 + \cdots}
   \]
Transcribed Image Text:**Tactics Box 7.1: Finding the Center of Gravity** 1. **Choose an origin for your coordinate system.** You can choose any convenient point as the origin. 2. **Determine the coordinates \((x_1, y_1), (x_2, y_2), (x_3, y_3), \ldots\)** for the particles of mass \(m_1, m_2, m_3, \ldots\), respectively. 3. **The \(x\) coordinate of the center of gravity is** \[ x_{cg} = \frac{x_1 m_1 + x_2 m_2 + x_3 m_3 + \cdots}{m_1 + m_2 + m_3 + \cdots} \] 4. **Similarly, the \(y\) coordinate of the center of gravity is** \[ y_{cg} = \frac{y_1 m_1 + y_2 m_2 + y_3 m_3 + \cdots}{m_1 + m_2 + m_3 + \cdots} \]
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