Mechanics - centre of mass lamina

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To find the center of mass of a lamina with a removed triangular section and an attached mass, one can treat the square and triangle as separate bodies. The coordinates of the center of mass for each shape should be calculated, considering the triangle's negative mass due to its removal. The overall center of mass can then be determined by combining the coordinates of the square, triangle, and the attached mass. This method simplifies the process and provides a clear solution. Understanding the principles of combining centers of mass is essential for solving such problems effectively.
kolomsg
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hi, I'm stuck and I can't seem to find a simple solution to questions regarding how to find the centre of mass of a lamina.

for example:
A uniform lamina with mass/unit area 0.12grams/cm2 consists of a square of
side 80cm, with one corner at the origin O(0, 0) and other corners at B(80, 0),
C(80, 80) and D(0, 80). A triangle of material has been removed from one corner
by cutting a straight line from E(50, 0) to F(80, 40), and a particle of mass 0.5kg
is attached at C. Find the coordinates of the centre of mass.
If anyone could help me, that'd be much appreciated. thanks
 
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Welcome to PF!

Hi kolomsg! Welcome to PF! :smile:

Do you know how to find the coordinates of the centre of mass of several bodies, given that you know the coordinates of the centre of mass of each?

Apply that to the square, the triangle, and the particle, but with the triangle having negative mass! :wink:
 
hi, thanks a lot. it helped!
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

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