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Center of Mass Problem Common Problems

Fisikastudycenter.com- High School Physics Problems and Solutions Examples, Center of Mass problems. Length and area.
Problem 1
Find the center of mass of this shape!


Solution
The data:
l1 = 20, X1 = 20, Y1 = 10
l2 = 20, X2 = 60, Y2 = 10
l3 = 80, X3 = 40, Y3 = 20
l4 = 20, X4 = 0, Y4 = 30
l5 = 40, X5 = 40, Y5 = 40
l6 = 20, X6 = 80, Y6 = 30

The center of the mass (X0 , Y0)




Problem 2
Find the location of Yo of the center of the mass of this shape below!



Solution
Get the data first:
Shape 1 (the black one)
A1 = (20 x 60) = 1200
Y1 = 30
Shape 2 (the blue one)
A2 = (20 x 60) = 1200
Y2 = (60 + 10) = 70


Problem 3
Find the ordinate location of the center of the mass from fig below!


Solution
First we have to divide this shape into 2 parts. A square on the bottom, and a triangle over it. Here are the data that we can get:
Data :
Shape 1 (a square)
A1 = (90 x 90) = 8100
Y1 = 90/2 = 45
Shape 2 (triangle)
A2 = 1/2(90 x 90) = 4050
Y2 = 1/3(90) + 90 = 120

The location of Yo :


Problem 4
Find the location of Yo of the center of the mass of below shape



Solution
Divide the shape into to parts. First, full shape (a rectangle without removed triangle area), second a hole forms triangle.
The data needed :
Shape 1
A1 = (180 x 90) = 16200
Y1 = (180/2) = 90
Shape 2
A2 = 1/2(90 x 90) = 4050
Y2 = 180 − (90/3) = 150

Location of Yo :


Problem 5
A cylinder and a cone are arranged shown below fig.



Find the center of mass location with AB as the reference line!

Solution
Data :
Shape 1 (cylinder)
V1 = π r2 t = 12π r2
X1 = 6
Shape 2 (cone)
V2 = 1/3 π r2 t = 4 π r2
X2 = 12 + (1/4 t) = 12 + 3 = 15

Xo location:

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