# Calculating Center of Mass with Added Particles

• phospho
In summary, you found the center of mass of the frame, and then calculated the mass ratio for the BC, BA, and AC.
phospho
http://examsolutions.co.uk/a-level-maths-papers/Edexcel/Mechanics/Mechanics-M2/2010-June/paper.php

Question 3)

part a) I got the answer to be 2.5 which is correct

part b) I don't really get how to do this, I understand as a new particle is being added which is the same mass of the total frame that the center of mass will change, but how do I figure out how much it will change by?

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phospho said:
part b) I don't really get how to do this, I understand as a new particle is being added which is the same mass of the total frame that the center of mass will change, but how do I figure out how much it will change by?
Just like you found the center of mass of the frame by finding the combined center of mass of its pieces, treat the added mass and the frame as two pieces. If you have two equal masses, where will the combined center of mass be?

The center of mass of two objects of different masses can be calculated as the weighted average of the two centers of mass, "weighted" by their masses.

Doc Al said:
Just like you found the center of mass of the frame by finding the combined center of mass of its pieces, treat the added mass and the frame as two pieces. If you have two equal masses, where will the combined center of mass be?

hm well the total mass is 32 as I figured out from part a), and if I do the same thing as I did in part a):

center of BC is (6,0), center of BA is (3,4), center of AC(9,4)

mass ratio for BC will be M, BA, 10, AC, 10 as M is the total mass which I found to be 32 in part a) then taking moments about B to find y bar:

32*0 + 10*4 + 10 * 4 = 32y
80/32 = y = 2.5 which is the same as part a :s

You already found the center of mass of the frame. (No need to start from scratch.) Treat that as mass 1. (What are its coordinates?) Treat the added mass as mass 2. What are its coordinates? Now find the center of mass of those two together.

To find the centre of mass of two bodies (or groups of bodies) of different mass, find the "weighted" average of the centres of mass, weighted by the mass of each part. That is, if the tow bodies have masses m1 and m2 and the x coordinates of centres of mass are x1 and x2 respectively, then the x coordinate of the centre of mass of both is [m1/(m1+m2)]x1+ [m2/(m1+m2)]x2= (m1x1+ m2x2)/(m1+m2).

got it, thank you both

## What is "Centre of mass confusion"?

"Centre of mass confusion" refers to a phenomenon where there is confusion or misunderstanding about the concept of center of mass in physics.

## Why is center of mass important?

The center of mass is important because it helps us understand the motion and stability of objects. It is also a key concept in many areas of physics, including mechanics, thermodynamics, and electromagnetism.

## How is center of mass calculated?

The center of mass is calculated by finding the weighted average of the positions of all the particles in a system. This can be done by multiplying the position of each particle by its mass and then dividing by the total mass of the system.

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

The center of mass and the center of gravity are often used interchangeably, but they are different concepts. The center of mass is the average position of all the mass in a system, while the center of gravity is the point at which the weight of an object can be considered to act.

## How does the center of mass affect an object's stability?

The lower the center of mass is, the more stable an object will be. This is because a lower center of mass means that the object is less likely to tip over or fall, as the weight is distributed closer to the ground. This is why most buildings and structures are designed with a low center of mass.

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