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

AI Thread Summary
The center of mass for a system of two point-like blocks is calculated using the formula (m1x1 + m2x2) / (m1 + m2), where m1 and m2 are the masses and x1 and x2 are their respective positions along the x-axis. This formula represents the weighted average position of the masses, accounting for their respective weights. Understanding the algebra behind this equation is crucial, as it reflects the mathematical definition of center of mass. The discussion emphasizes that the center of mass is not merely an average but a weighted average, where more massive components influence the position more significantly. Clarification of these concepts can often be found in standard mechanics textbooks.
sweatband
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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

 
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What is the general formula / definition of center of mass ?
 
Are you questioning the definition of center of mass? Maybe this brief discussion will help: Center of Mass
 
Center of mass: The point that represents the "average" position of the entire mass of a system.
 
sweatband said:
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.
 
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
 
sweatband said:
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.
 
Awsome, the link answers my all my questions, thanks guys!
 
sweatband said:
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
 
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sweatband said:
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).
 
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