Finding the CG of a System with m1 & m2

[vscid]

If I have a body with mass m1, bolted to a body with mass m2, how do I find the CG of the entire system?
Thanks!

 

[HallsofIvy]

Find the CG of each separately, Then find the "weighted" average with each weighted by its mass. That is, using _x to mean "x-coordinate". CG_x= (m1CG1_x+ m2CG2_x)/(m1+ m2). The same is true for the y and z components.

 

[Moetasim]

To find the center of gravity (CG) of a system with two bodies, we can use the formula: CG = (m1*x1 + m2*x2)/(m1 + m2), where m1 and m2 are the masses of the bodies and x1 and x2 are their respective distances from a reference point.

First, we need to determine a reference point for the system. This can be any point on the system, but it is usually helpful to choose a point that is easy to measure from or that has a known value, such as the point of attachment between the two bodies.

Next, we need to measure the distances x1 and x2 from the reference point to the center of mass of each body. This can be done by balancing the bodies on a pivot point and measuring the distance from the pivot to the center of mass. Alternatively, if the bodies are simple geometric shapes, we can use their dimensions to calculate the distances.

Once we have the values for m1, m2, x1, and x2, we can plug them into the formula to calculate the CG of the entire system. This will give us a single point that represents the average location of the mass of the entire system.

It is important to note that the CG may not always fall within the physical boundaries of the bodies, especially if they are irregularly shaped or have significantly different masses. However, it is still a useful point for understanding the overall behavior and stability of the system.