Three solid, uniform boxes are aligned as in the figure below. Find the X- and y-coordinates (in m) of the center of mass of the three boxes, measured from the bottom left corner of box A. (Consider the three-box system.) HINT x cm Y cm || Origin m m 0.360 m A 0.750 kg 0.420 m B 1.00 kg 0.240 m с 0.650 kg 0.410 m X

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**Problem Statement:**

Three solid, uniform boxes are aligned as shown in the figure. Find the x- and y-coordinates (in meters) of the center of mass of the three boxes, measured from the bottom left corner of box A. (Consider the three-box system.)

**Diagram Explanation:**

The diagram shows three adjacent boxes labeled A, B, and C from left to right. The x- and y-coordinate system is indicated, with the origin at the bottom left corner of box A.

- **Box A**:
  - Width: 0.360 m
  - Mass: 0.750 kg

- **Box B**:
  - Width: 0.420 m
  - Mass: 1.00 kg

- **Box C**:
  - Width: 0.240 m
  - Height: 0.410 m
  - Mass: 0.650 kg

**Objective:**

To calculate the center of mass (x_cm, y_cm) of the entire three-box system.

**Formulas:**

The center of mass coordinates \((x_{cm}, y_{cm})\) are given by:

\[ 
x_{cm} = \frac{(m_1 \cdot x_1) + (m_2 \cdot x_2) + (m_3 \cdot x_3)}{m_1 + m_2 + m_3}
\]

\[ 
y_{cm} = \frac{(m_1 \cdot y_1) + (m_2 \cdot y_2) + (m_3 \cdot y_3)}{m_1 + m_2 + m_3}
\]

where \(m_1, m_2, m_3\) are the masses of boxes A, B, and C respectively, and \((x_1, y_1), (x_2, y_2), (x_3, y_3)\) are the coordinates of the centers of the individual boxes.

**Inputs for Calculation:**

- Box A center: (\(0.180, 0\))
- Box B center: (\(0.570, 0\))
- Box C center: (\(0.810, 0.205\))

**Solution:**

Calculate \(x_{cm}\) and \(y_{cm}\)
Transcribed Image Text:**Problem Statement:** Three solid, uniform boxes are aligned as shown in the figure. Find the x- and y-coordinates (in meters) of the center of mass of the three boxes, measured from the bottom left corner of box A. (Consider the three-box system.) **Diagram Explanation:** The diagram shows three adjacent boxes labeled A, B, and C from left to right. The x- and y-coordinate system is indicated, with the origin at the bottom left corner of box A. - **Box A**: - Width: 0.360 m - Mass: 0.750 kg - **Box B**: - Width: 0.420 m - Mass: 1.00 kg - **Box C**: - Width: 0.240 m - Height: 0.410 m - Mass: 0.650 kg **Objective:** To calculate the center of mass (x_cm, y_cm) of the entire three-box system. **Formulas:** The center of mass coordinates \((x_{cm}, y_{cm})\) are given by: \[ x_{cm} = \frac{(m_1 \cdot x_1) + (m_2 \cdot x_2) + (m_3 \cdot x_3)}{m_1 + m_2 + m_3} \] \[ y_{cm} = \frac{(m_1 \cdot y_1) + (m_2 \cdot y_2) + (m_3 \cdot y_3)}{m_1 + m_2 + m_3} \] where \(m_1, m_2, m_3\) are the masses of boxes A, B, and C respectively, and \((x_1, y_1), (x_2, y_2), (x_3, y_3)\) are the coordinates of the centers of the individual boxes. **Inputs for Calculation:** - Box A center: (\(0.180, 0\)) - Box B center: (\(0.570, 0\)) - Box C center: (\(0.810, 0.205\)) **Solution:** Calculate \(x_{cm}\) and \(y_{cm}\)
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