How Is the Center of Mass Calculated for Two Point-Like Blocks?

[sweatband]

Homework Statement

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.

Homework 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?

The Attempt at a Solution

 

[malawi_glenn]

What is the general formula / definition of center of mass ?

 

[Doc Al]

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

 

[sweatband]

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

 

[malawi_glenn]

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

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

 

[sweatband]

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

 

[malawi_glenn]

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

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.

 

[sweatband]

Awsome, the link answers my all my questions, thanks guys!

 

[malawi_glenn]

Awsome, the link answers my all my questions, thanks guys!

great that we could help you. But don't you own a book for the course? This is standard mechancs #1 :P

 

[Doc Al]

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

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).