How Do You Calculate the Center of Mass for Multiple Cubes?

AI Thread Summary
To calculate the center of mass (CM) for three cubes of sides 0, 20, and 30, placed in contact, the formula Xcm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3) is used. Since the cubes are made of the same uniform material, their masses can be determined by their volumes, which are proportional to the cube of their side lengths. Even without specific mass values, the ratios of their masses can be utilized to find the CM. By assuming any density, the calculated position of the CM remains consistent regardless of the density chosen. The solution confirms that the approach is valid as long as the density is uniform across the cubes.
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[SOLVED] Finding Center of mass

Homework Statement




Three cubes, of side 0, 20, and 30, are placed next to one another (in contact) with their centers along a straight line as shown in the figure. What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material and 0 = 2.5 cm.




Homework Equations



Xcm = m1x1 + m2x2.../ m1 + m2 +...

The Attempt at a Solution



it does not give the mass of the cubes, so i don't know how to relate to such a problem
 
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If they have the same density, then you may not know the masses, but you know the ratio of the masses. That's all you need to know. Assume any density you like and work it out. Now choose another density and work it out. You'll get the same answer.
 
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