Finding center of mass of a picture

AI Thread Summary
To find the center of mass (CoM) of a uniform sheet of steel, first determine the x and y coordinates separately by analyzing the mass distribution. The CoM is the point where mass is symmetrically arranged, meaning equal mass on either side of the chosen axis. For the x direction, identify the value where mass is evenly distributed, and do the same for the y direction. The final coordinates for the center of mass in this case are (7, 8). Understanding these principles is crucial for solving related problems effectively.
runawayshoes
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hey everyone, I am stumped as to finding the x and y coords of the center of mass of this picture. it is supposed to be a uniform sheet of steel in increments of 6. please help, i have an exam tomorrow.

p9-41alt.gif
 
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What exactly is the centre of mass?

Once you have the answer, you can "decompose" it into two components, x and y. So you'd basilcally find the centre line along x, then along y, and your centre point would be the intersection of the two.
 
i'm still stumped heh
 
Find the CoM in each direction seperately. Meaning stack all the blocks so that you only have one direction to deal with at a time. For example, imagine a figure with 3m on the left column, 2m in the middle column, and 1m on the right column (where m is the mass of one block). then find the center of mass of those 3 blocks, this corresponds to the CoM in the x direction. Do something similar for the y direction.
 
The centre of mass is a point around which all the mass is symmetrically arranged.

Take the x direction for example. For what value of x would the mass be symmetrically distributed, i.e. you have the same mass to the right and to the left of your x value?

Note that if you balance your plate on a knife edge placed at that x, the plate would be in equilibrium.
 
i got it, thanks. answer is (7,8) btw
 
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