Math Problem Statement

The center of mass is

enter your response here.

​(Type an ordered​ pair, Type an exact​ answer.)

Solution

To determine the center of mass (xˉ,yˉ)(\bar{x}, \bar{y}), use the formulas:

xˉ=miximi,yˉ=miyimi\bar{x} = \frac{\sum m_i x_i}{\sum m_i}, \quad \bar{y} = \frac{\sum m_i y_i}{\sum m_i}

where:

  • mim_i are the masses
  • (xi,yi)(x_i, y_i) are the corresponding coordinates

If you provide the masses and their coordinates, I can compute the exact center of mass for you.

Would you like to share the values?

Related Questions:

  1. What is the difference between the centroid and the center of mass?
  2. How do you find the center of mass of a continuous object?
  3. What happens if the masses are not uniform in distribution?
  4. How does center of mass apply in physics and engineering?
  5. How do you calculate the center of mass in three dimensions?

Tip: The center of mass is the point where an object balances perfectly if supported!

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Math Problem Analysis

Mathematical Concepts

Physics
Center of Mass
Coordinate Geometry

Formulas

\bar{x} = \frac{\sum m_i x_i}{\sum m_i}
\bar{y} = \frac{\sum m_i y_i}{\sum m_i}

Theorems

Center of Mass Theorem

Suitable Grade Level

Grades 9-12