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:
- Plotting the positions of three particles on a 2D coordinate system.
- Calculating the center of mass (COM) of these particles.
Given data:
- Particle positions and masses:
- Particle 1: Mass = , Position =
- Particle 2: Mass = , Position =
- Particle 3: Mass = , Position =
Step 2: Formula for Center of Mass
The center of mass coordinates are calculated as: Where represent the mass and position coordinates of each particle.
Step 3: Calculate Center of Mass
Total Mass:
:
:
[ 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
-
Suitable Grade Level
Grades 10-12