Linear Mass Density - Bars (Center of Mass)

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SUMMARY

The discussion focuses on calculating the center of mass for four black bars with constant linear density, specifically in a square configuration. The key formula used is M0 X = summation of (MiXi), where M represents the mass of a bar of length L. The answer key indicates that the mass at the center is M/sqrt(2) located at coordinates (L/4, L/4) and (L/4, 3L/4). This is due to the diagonal length of the square being L√2, leading to a reduced mass for the smaller bars along the diagonals.

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1. Homework Statement
The 4 black bars have constant linear density. In terms of L, find the coordinate of the center of mass

Homework Equations


M0 X = summation of (MiXi)

The Attempt at a Solution


I understand most of the solution, except the answer key says one thing I don't get
M/sqrt(2) at (L/4, L/4)
and at (L/4, 3L/4).
Why is there less mass in the middle of bar though the bar is uniform?
 
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M is the mass of a bar of length L. The diagonal of the square is L√2. Half the diagonal is L/√2. That's the length of each of the smaller little bars along the diagonals. So their masses must be M/√2.

Chet
 
Thanks! That made a lot of sense.
 

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