Center of Mass involving three cubes

In summary, the problem is asking for the position of the center of mass for a system of three cubes of different sizes, all made of the same uniform material. The equation for center of mass is provided, and the challenge lies in determining the masses and positions of the cubes. After considering the cubes' densities and using the equation, the position of the center of mass can be determined.
  • #1
DLPhysics
11
0

Homework Statement


Three cubes, of side l, 2l, and 3lo, are placed next to one another (in contact) with their centers along a straight line and the l = 2lo cube in the center. What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material.


Homework Equations


CM = (m1x1 + m2x2 + m3x3)/ (m1 + m2 + m3)


The Attempt at a Solution



The one thing that stumped me the most was how to find the mass of the object. I'm inferring that since the cubes are all made out of the same material, they have the same density, meaning that the masses have an inverse-square relationship with each other.

And I have trouble determining the positions of the boxes; I always go by the center of the objects, correct?

Damion
 
Physics news on Phys.org
  • #2
I figured out the problem on my own! Ahh, it was simpler than I thought it would be.
 

1. What is the definition of "center of mass"?

The center of mass is a point within a system of objects that represents the average location of the mass of the system. It is the point at which the entire mass of the system can be considered to be concentrated.

2. How is the center of mass calculated for three cubes?

The center of mass for three cubes can be calculated by finding the average position of the three cubes. This can be done by finding the midpoint of each cube's length, width, and height, and then calculating the average of these coordinates.

3. What factors affect the center of mass of three cubes?

The center of mass of three cubes is affected by the mass and position of each cube. The closer a cube is to the center of mass, the greater its effect on the overall location of the center of mass. Additionally, the size and shape of each cube can also affect the center of mass.

4. How does the center of mass change when the cubes are stacked in different configurations?

The center of mass will change depending on the configuration of the cubes. When the cubes are stacked on top of each other, the center of mass will shift towards the bottom of the stack. When the cubes are arranged in a line, the center of mass will be in the middle of the line.

5. Why is the center of mass important in physics?

The center of mass is important in physics because it helps us understand the overall motion and stability of a system. It is used in various calculations, such as determining the torque and momentum of an object. It also helps us predict how a system will behave under different forces and interactions.

Similar threads

How to find the center of mass of a cube?
    • Introductory Physics Homework Help
Replies
6
Views
6K
Center of Mass (Subtraction over addition)
    • Introductory Physics Homework Help
Replies
7
Views
2K
Determine the location of the center of mass of spheres
    • Introductory Physics Homework Help
Replies
3
Views
5K
Finding the center of mass of a homogeneous object
    • Introductory Physics Homework Help
Replies
6
Views
3K
Finding the POSITION of the center of mass
    • Introductory Physics Homework Help
Replies
2
Views
1K
Torque with 2D center of mass
    • Introductory Physics Homework Help
Replies
3
Views
1K
Calculating Center of Mass in NH3 Molecule
    • Introductory Physics Homework Help
Replies
4
Views
6K
Displacement of Center of Mass Problem
    • Introductory Physics Homework Help
Replies
3
Views
3K
Period of a physical pendulum with a pivot at its center
    • Introductory Physics Homework Help
Replies
3
Views
2K
Find the centre of mass of the system?
    • Introductory Physics Homework Help
Replies
23
Views
2K

Hot Threads

Recent Insights

Back
Top