# How do you find the Center of mass of an object like this?

1. Apr 21, 2007

### skittlez411

how do you find the Center of mass of an object like this??

1. The problem statement, all variables and given/known data

Find the location of the center of mass for the system of particles below.

2. Relevant equations

3. The attempt at a solution

tried to use Xcm= 1/(M1+M2)*(M1+M2) but im stuck.

2. Apr 22, 2007

They all equal in value?

3. Apr 22, 2007

### skittlez411

yes they are all equal sorry about the picture..

4. Apr 22, 2007

You can join the segments of the object to make diffent sections that you can add to get your center of mass. Also represent each mass as a variable, because you say they are the same, don't they all have the same mass? What is the total mass? Don't you have to find the center of mass in the x and in the y direction?

5. Apr 22, 2007

### DaveC426913

Is the picture a rough diagram? I am presuming that all blocks are supposed to be the same size.

How I would find the centre of mass is hang it from an adjustable piece of string near the centre. When the object is horizontal, the string is at the CoM.

This doesn't help you I know, I've always been interested in analog problem-solving.

Last edited: Apr 22, 2007
6. Apr 22, 2007

### skittlez411

yah im sorry about the diagram, this is the best i could do. They're all the same size and same mass.

So i still dont really understand.. how do i combine them?

7. Apr 22, 2007

### denverdoc

simple weighted mean, along the x axis, choose the center were the blocks are,

then just multiply the moments by the area.

ie, -3*4+-1*2+-1*1+0*3 and same for right hand side, divide by total number of squares. Again weighted average. From symmetry its gonna be in the middle for x, do same for Y, Cm are these coordinates.

8. Apr 22, 2007

### skittlez411

hmm... still dont quite get it..

9. Apr 22, 2007

Here's a hint: There are 5 pieces.

10. Apr 22, 2007

### skittlez411

ok... my approach is there are 5 pieces, and then 10 pieces... but after that im stuck still...

11. Apr 22, 2007

### denverdoc

Ok I'll try again, its a torque problem. Imagine two weights on a seesaw. The two kids weigh different, find the point where they balance.

12. Apr 22, 2007

distance for each from the point you want to referance from(like an origin on a graph) for each direction of x or y. find the middle of the objects on the x directions and in the y directions. Distances from the orgin to the middle of each object for each dimention. add the multipuls of the mass of the objects times the distance to the center(for each direction). Divide by the total mass for each directional center of mass. You will see the mass cancel out.

Last edited: Apr 22, 2007
13. Apr 22, 2007

### skittlez411

k so i got CM of the 2 pieces is 3/2L apart.
CM is (5/15)(3/2L)=1/2 above the center of mass of those 5 pieces.

what abt the rest of the squares? does this make sense?

14. Apr 22, 2007