Displacement of Center of Mass Problem

[halo168]

1. The problem statement, all variables, and given/known data
A square of side 2 L is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C’. The displacement of the y coordinate of the center of mass (from C to C’) is:

Homework Equations

x_cm=Σmx/Σm

The Attempt at a Solution

M/4 = mass of the quarter of the main square that is off center
L/4 = distance off from center
3M/4= total mass of the new object

Xcm = (M/4)(L/4)/(3M/4)=(1/12)L
Ycm = (M/4)(L/4)/(3M/4)=(1/12)L

Therefore, the displacement is sqrt(2)/12 by Pythagorean Theorem. I'm not sure why L/4 = distance off from center (what point is L/4 off from the center and how is it found?), but it's the only one that works. Can someone please explain?

 

[mfb]

How can you remove a square with longer sides than the original, full square? Based on your calculations I guess it should be L/2?

I'm not sure why L/4 = distance off from center (what point is L/4 off from the center and how is it found?), but it's the only one that works.

Did you draw a sketch and mark the centers?

 

[halo168]

How can you remove a square with longer sides than the original, full square? Based on your calculations I guess it should be L/2?Did you draw a sketch and mark the centers?

Yes, please refer to the following document: https://docs.google.com/document/d/1cvykDUr0kWsPhmI5sb-63-RNlahr6_8vUVbNrIs9HNA/edit?usp=sharing

 

[mfb]

Divide the remaining area into three squares. It should be obvious that their centers are L/4 to the left/right/top/bottom relative to the center.