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

In summary, to find the center of gravity of three balls with masses of 5 g, 1 g, and 7 g respectively, that are connected by massless rods, you can use the equations for center of mass for particles in the x and y directions. By plugging in the values and solving, the center of gravity can be determined to be at the coordinates (4.54, 4.6) on the graph. This can also be found by taking the sum of the equations for center of mass and breaking them down into y and x components, as shown in the online example provided.
  • #1
Shadow_C316
6
0
Three balls with masses of 5 g, 1 g, and 7 g,
respectively, are connected by massless rods.
The balls are located (in meter intervals) as
in the figure.

Imagine the first quadrant of a graph.
The 5 gram is at point (3,8)
The 7 gram is at point (5,2)
The 1 gram is at point (9,6)

What do do to find the center of gravity? I've looked online and I only see formulas for 2 objects instead of 3 so I'm stuck. Forgot to say they are all connected by massless rods.
 
Last edited:
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  • #2
the sum of the equations...
 
  • #3
Sum of what equations?
 
  • #4
the sum of the center mass equation... and you got to break it down into y and x... there is an similar example online, i'll look it up for you
 
  • #6
Thanks so much! Would the answer be:

In the X direction
((5x3) + (7x5) + (1x9))/13=4.54

In the Y direction
((5x8) + (7x2) + (1x6))/13=4.6
 

FAQ: How Do You Calculate the Center of Mass for Multiple Objects?

What is the center of mass and why is it important?

The center of mass is the point at which an object's mass is evenly distributed in all directions. It is important because it helps determine the overall stability and motion of an object.

How do I calculate the center of mass?

The center of mass can be calculated by taking the sum of the individual masses multiplied by their respective distances from a chosen reference point, and then dividing by the total mass of the system.

What factors affect the center of mass?

The center of mass is affected by the distribution of mass within an object, as well as any external forces acting on the object.

What is the difference between center of mass and center of gravity?

The center of mass is the point at which an object's mass is evenly distributed, while the center of gravity is the point at which the force of gravity can be considered to act on an object. In most cases, these two points are in the same location, but they may differ in situations where there are varying gravitational forces acting on different parts of the object.

How can I use the center of mass to solve real-world problems?

The center of mass can be used to determine the balance and stability of structures, vehicles, and other objects. It can also be used to analyze the motion and trajectory of objects in motion, such as projectiles or satellites.

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