Finding center of mass of a picture

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SUMMARY

The center of mass (CoM) of a uniform sheet of steel can be determined by decomposing the mass distribution into x and y components. To find the CoM, one must calculate the center line along the x-axis and y-axis separately, identifying the intersection as the CoM. For example, if the mass distribution consists of 3m, 2m, and 1m in respective columns, the CoM in the x direction can be calculated, leading to the final coordinates of (7, 8) for this specific case.

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  • Understanding of center of mass concepts
  • Basic knowledge of mass distribution
  • Ability to perform coordinate calculations
  • Familiarity with equilibrium principles
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  • Study the mathematical formulation of center of mass in two dimensions
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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 separately. 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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