Math Problem Statement
Three masses of 5 kg, 9 kg, and 12 kg are placed at (-4, 3), (2, 2) , and (5, 0) respectively. Find the center of mass.
Solution
To find the center of mass of the system of three masses, we use the formula for the coordinates of the center of mass:
where is the mass and are the coordinates of the masses.
Given:
- Mass at coordinates
- Mass at coordinates
- Mass at coordinates
Step 1: Find
Step 2: Find
Thus, the center of mass is approximately at .
Would you like more details or have any questions?
Related Questions:
- How does changing the mass at a specific point affect the center of mass?
- What if the mass distribution were in 3D? How would we calculate the center of mass?
- How do we calculate the center of mass for continuous distributions?
- What happens if one mass is at the origin?
- Can the center of mass lie outside the system of particles?
Tip:
The center of mass is a balance point, so it can be useful in analyzing the motion of the entire system in physics problems.
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Math Problem Analysis
Mathematical Concepts
Physics
Center of Mass
Weighted Averages
Coordinate Geometry
Formulas
x_cm = (Σ(m_i * x_i)) / Σ(m_i)
y_cm = (Σ(m_i * y_i)) / Σ(m_i)
Theorems
Center of Mass Formula
Suitable Grade Level
Grades 10-12