How to Calculate Gravity Center of Two Objects?

How to Calculate Gravity Center of Two Objects?

In general, systems are designed from multiple parts. Multiple parts are working together to create useful work for the civilization. So, the center of gravity is calculated with the calculation of the separate parts of a system. Think about the machinery that has lots of kinds of parts. In the calculation of the center of gravity of this machinery, the center of gravities of all the parts must be calculated to find the total gravity center of the machinery. In this article, we elaborate on the calculation of the gravity centers of two objects. 

Once we lose our gravitational center, we fall(Image Source: Wikimedia)

Calculation of Gravity Center of Two Objects

In the calculation of the center of gravities of two objects, first, we need to calculate the center of gravity of these objects separately. Think about a situation where we have two objects in the space which has the coordinates and masses of;

A: (x, y, z) = (5, 10, 15), Mass = 10kg 

B: (x, y, z) = (-3, 3, 2), Mass = 20kg

To calculate the total center of gravity of these two masses, we need to find the total center of gravity of all the coordinates separately.

Gravity center of X coordinate; 

Gx = (Ma*Xa + Mb*Xb)/(Ma+Mb);

= 5*10 + (-3*20) = -10

Gx = -10/(10+20) = -0.33. 

In this calculation, first, we found the effects of all the masses on the place of the center of gravity on the X coordinate. We multiplied all the X coordinates with masses and we summed up them. To find the exact place of the gravity center of the X coordinate, we divided this value by the total mass. And Gx is found as -0.33.

Let’s do the same thing for the Y coordinate.

Gy = (Ma*Ya + Mb*Yb)/(Ma+Mb);

= 10*10 + 20*3 = 160; 

Gy = 160/(10+20) = 5.33. 

We made exatcly the same calculation that we made for the X coordinates. We just changed the coordinates. And finally, lets calculate the gravity center in the Z coordinate.

Gz = (Ma*Za + Mb*Zb)/(Ma+Mb);

= 10*15 + 20*2 = 190; 

Gz = 190(10+20) = 6.33.

As a result, the total center of gravity of these two objects in the space can be given as; 

Gtotal = (Gx, Gy, Gz) = (-0.33, 5.33, 6.33), 30kg. 

If there is a machinery that is constituted with these parts, mass of this machinery will be 30 kg and its gravity center will at -0.33, 5.33, 6.33 coordinates. 

You Can Use the Center of Gravity Calculator

We prepared a center of gravity calculator that you can easily calculate these kinds of calculations. You can calculate the center of gravities of 2D and 3D objects easily. And then you just need to enter the masses of how many objects you are calculating. After entering all the masses, the calculator will ask the coordinates of these masses in X, Y, and Z if you selected the 3D calculation. Then click on the ‘Calculate!’ button to see the result. If you want to make another calculation, just click on the ‘Reset’ button and re-enter the values. 

Conclusion

Calculation of the center of gravity of two objects is just simple as above.

Do not forget to leave your comments and questions about the calculation of the gravşty center of two objects. 

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