# Center of Mass Problem

1. ### sweatband

16
1. The problem statement, all variables and given/known data

Consider a system of two blocks that have masses m_1 and m_2. Assume that the blocks are point-like particles and are located along the x axis at the coordinates x_1 and x_2. In this problem, the blocks can only move along the x axis. Find the x coordinate of the center of mass of the system.

2. Relevant equations

The solution is ( $$\((m1x1 + m2x2)/(m1 + m2)$$, but I cannot for the life of me understand why this is exactly. Why multiply the mass by the x-coordinate of its location?

3. The attempt at a solution

Last edited: Nov 2, 2007
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3. ### malawi_glenn

4,727
What is the general formula / definition of center of mass ?

### Staff: Mentor

Are you questioning the definition of center of mass? Maybe this brief discussion will help: Center of Mass

5. ### sweatband

16
Center of mass: The point that represents the "average" position of the entire mass of a system.

6. ### malawi_glenn

4,727
well hmm yes and no, i meant: formulate it with an expression.
See the link that Doc Al posted.

7. ### sweatband

16
What I don't understand is the algebra of arriving at that equation, and thanks for that link, Doc Al, I'm looking over it now

8. ### malawi_glenn

4,727

Well the thing is that the definition is purley mathametical, and trying to explain it in words are just secondary. The definition of center of mass is the formulas that is posted on that link.

16

10. ### malawi_glenn

4,727
great that we could help you. But dont you own a book for the course? This is standard mechancs #1 :P

### Staff: Mentor

You can think of it (loosely) as the weighted average position of the mass in a system. Not just the average. A part of the system with twice the mass (as some other part) gets counted twice (compared to that other part).