Math Problem Statement

Tiga partikel bermassa yang beragam berada dalam sistem koordinat dua dimensi (x dan y). Gambarkan posisi ketiga partikel dalam sistem koordinat, dan tentukan pusat massanya.

Solution

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 = 1.2kg1.2 \, \text{kg}, Position = (0,0)(0, 0)
    • Particle 2: Mass = 2.5kg2.5 \, \text{kg}, Position = (140,0)(140, 0)
    • Particle 3: Mass = 3.4kg3.4 \, \text{kg}, Position = (70,120)(70, 120)

Step 2: Formula for Center of Mass

The center of mass coordinates (xCOM,yCOM)(x_\text{COM}, y_\text{COM}) are calculated as: xCOM=miximi,yCOM=miyimix_\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 mi,xi,yim_i, x_i, y_i represent the mass and position coordinates of each particle.


Step 3: Calculate Center of Mass

Total Mass:

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

xCOMx_\text{COM}:

xCOM=(1.2×0)+(2.5×140)+(3.4×70)7.1x_\text{COM} = \frac{(1.2 \times 0) + (2.5 \times 140) + (3.4 \times 70)}{7.1} xCOM=0+350+2387.1=5887.182.82cmx_\text{COM} = \frac{0 + 350 + 238}{7.1} = \frac{588}{7.1} \approx 82.82 \, \text{cm}

yCOMy_\text{COM}:

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

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Math Problem Analysis

Mathematical Concepts

Physics
Coordinate Geometry
Center of Mass

Formulas

x_COM = (Σm_i * x_i) / Σm_i
y_COM = (Σm_i * y_i) / Σm_i

Theorems

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Suitable Grade Level

Grades 10-12