# Two rigid bodies combined center of gravity

• co0ldood
In summary, the two objects with different weight will have a combined CoG that is located somewhere between the centroid of each object.
co0ldood
Hello all. I'm trying to find the equation for combined Center of Gravity (CoG) when you combine two objects with different weight.

I know how to find the centroid, which is what the CoG would be if both objects were the same weight.

But what about two objects with different weight? For an example, I have two square with the area of x^2. Square A weights 40lbs and square B weights 600lbs. If I combined both squares, where would the CoG be?

I'm assuming the equation has something to do with density, distance of CoG at a specific point, and area invovled. Thanks for the help!

Consider the straight line connecting the CoG's of the 2 items. Find a point on the line where mass times distance (from the individual CoG to that point) is the same for both weights.

co0ldood said:
Hello all. I'm trying to find the equation for combined Center of Gravity (CoG) when you combine two objects with different weight.

I know how to find the centroid, which is what the CoG would be if both objects were the same weight.

But what about two objects with different weight? For an example, I have two square with the area of x^2. Square A weights 40lbs and square B weights 600lbs. If I combined both squares, where would the CoG be?

I'm assuming the equation has something to do with density, distance of CoG at a specific point, and area invovled. Thanks for the help!

Is this related to the tipping forklift issue at work?

It would help if you could show us a diagram of what you are asking, but I'll take a try at some hints to help you out. Think of a teeter-totter -- it's balanced when the two weights at the ends are equal, right? Now what if the fulcrum were moved closer to the left weight? How would the two end weights have to be related in order to still balance?

The concept you use in the above question is "balancing the torques" or balancing the moments. Torque is force X distance. Do you see how balancing the two torques will make the teeter-totter balance? Can you see how this applies to your COG question?

BTW, I appreciate you mentioning in your other forklift thread that it's okay to move the thread to the Homework Help forums. The threads may still get moved, but I'll leave this here for now.

berkeman said:
Is this related to the tipping forklift issue at work?

It would help if you could show us a diagram of what you are asking, but I'll take a try at some hints to help you out. Think of a teeter-totter -- it's balanced when the two weights at the ends are equal, right? Now what if the fulcrum were moved closer to the left weight? How would the two end weights have to be related in order to still balance?

The concept you use in the above question is "balancing the torques" or balancing the moments. Torque is force X distance. Do you see how balancing the two torques will make the teeter-totter balance? Can you see how this applies to your COG question?

BTW, I appreciate you mentioning in your other forklift thread that it's okay to move the thread to the Homework Help forums. The threads may still get moved, but I'll leave this here for now.

Thanks mathman and berkeman. I see how it's related. I'm not sure why I didn't think of that. Must be late in the day!

BTW, good memory berkeman! I'm in transition in putting theory into practice and seeing how everything works out. I've already obtained my answer so hopefully someone else may learn something useful out of these scenarios.

I'm trying to be as broad as I can so I don't leak out anything I'm working on directly. Hope you undrestand! Thanks again.

## 1. What is the center of gravity of two rigid bodies combined?

The center of gravity of two rigid bodies combined is the point where the combined weight of both bodies is evenly distributed. It is also known as the center of mass.

## 2. How is the center of gravity of two rigid bodies combined calculated?

The center of gravity of two rigid bodies combined can be calculated by finding the weighted average of the individual centers of gravity of each body. The formula is: (m1 x d1 + m2 x d2) / (m1 + m2) where m1 and m2 are the masses of the two bodies and d1 and d2 are the distances of their respective centers of gravity from a reference point.

## 3. What factors affect the center of gravity of two rigid bodies combined?

The center of gravity of two rigid bodies combined is affected by the masses of the two bodies and their respective distances from a reference point. The shape and orientation of the bodies can also have an impact on their combined center of gravity.

## 4. Why is the center of gravity of two rigid bodies combined important?

The center of gravity of two rigid bodies combined is important because it helps determine the stability and balance of the combined system. It is also used in calculations for various engineering and physics applications, such as designing structures and predicting the motion of objects.

## 5. Can the center of gravity of two rigid bodies combined be outside of the physical bodies?

Yes, the center of gravity of two rigid bodies combined can be outside of the physical bodies. This can happen if the two bodies have different masses and/or if they are not symmetrical. In this case, the center of gravity will be located somewhere between the two bodies, but not necessarily within either of them.

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