Step 1: Problem Breakdown

The question involves:

1. Plotting the positions of three particles on a 2D coordinate system.
2. Calculating the center of mass (COM) of these particles.

Given data:

• Particle positions and masses:
  • Particle 1: Mass = $1.2 \, \text{kg}$, Position = $(0, 0)$
  • Particle 2: Mass = $2.5 \, \text{kg}$, Position = $(140, 0)$
  • Particle 3: Mass = $3.4 \, \text{kg}$, Position = $(70, 120)$

Step 2: Formula for Center of Mass

The center of mass coordinates $(x_\text{COM}, y_\text{COM})$ are calculated as: $x_\text{COM} = \frac{\sum m_i x_i}{\sum m_i}, \quad y_\text{COM} = \frac{\sum m_i y_i}{\sum m_i}$ Where $m_i, x_i, y_i$ represent the mass and position coordinates of each particle.

Step 3: Calculate Center of Mass

Total Mass:

$\text{Total mass} = 1.2 + 2.5 + 3.4 = 7.1 \, \text{kg}$

$x_\text{COM}$:

$x_\text{COM} = \frac{(1.2 \times 0) + (2.5 \times 140) + (3.4 \times 70)}{7.1}$ $x_\text{COM} = \frac{0 + 350 + 238}{7.1} = \frac{588}{7.1} \approx 82.82 \, \text{cm}$

$y_\text{COM}$:

[ y_\text{COM} = \frac{(1