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

Click For Summary
SUMMARY

The center of mass (CM) for a system of three cubes with side lengths of 0 cm, 20 cm, and 30 cm can be calculated using the formula Xcm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3). Given that the cubes are made of the same uniform material, their masses can be determined by their volumes, which are proportional to the cubes' side lengths. By assuming any density, the calculated position of the CM remains consistent, demonstrating that the specific density does not affect the outcome.

PREREQUISITES
  • Understanding of center of mass calculations
  • Familiarity with basic geometry and volume calculations
  • Knowledge of uniform density concepts
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the derivation of the center of mass formula for composite objects
  • Explore the impact of varying densities on center of mass calculations
  • Learn about the application of center of mass in physics and engineering
  • Investigate numerical methods for calculating center of mass in complex shapes
USEFUL FOR

Students in physics or engineering courses, educators teaching mechanics, and anyone interested in understanding the principles of center of mass in multi-object systems.

Oomair
Messages
36
Reaction score
0
[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
 
Physics news on Phys.org
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.
 

Similar threads

How to find the center of mass of a cube?
  • · Replies 6 ·
Replies
6
Views
7K
Center of Mass (Subtraction over addition)
  • · Replies 7 ·
Replies
7
Views
3K
Center of Mass involving three cubes
  • · Replies 1 ·
Replies
1
Views
6K
Determine the location of the center of mass of spheres
  • · Replies 3 ·
Replies
3
Views
5K
What Is the Minimum Coefficient of Friction for a Tilted Cube?
  • · Replies 3 ·
Replies
3
Views
2K
Displacement of Center of Mass Problem
  • · Replies 3 ·
Replies
3
Views
3K
Center of Mass - Man on Boat Homework help
  • · Replies 7 ·
Replies
7
Views
7K
Find the center of mass of a plate
  • · Replies 57 ·
2
Replies
57
Views
6K
Center of mass for two small particles
  • · Replies 4 ·
Replies
4
Views
5K
Center of Mass Rowboat Question
  • · Replies 4 ·
Replies
4
Views
3K