- #1
Lone Wolf
- 10
- 1
- Homework Statement
- Find the coordinates of the center of mass of the object represented in the figure.
- Relevant Equations
- Equation of the center of mass.
The object is:
My attempt at a solution:
I divided the object into 3 different rectangles and found the coordinates for the center of mass of each one, considering the origin at point "O".
Then I found the mass of each rectangle, assuming the object has an area density of σ.
m1 = 15σ; m2= 6σ; m3 = 8σ.
After that I applied the center of mass position equation for x and y coordinates.
rx = (r1x*m1+r2x*m2+r3x*m3)/(m1+m2+m3) = (0.75*15σ+2.25*6σ+3.5*8σ)/(29σ) = 1.82
ry = (5*15σ + 9*6σ + 1*8σ)/(29σ) = 4.72
So the coordinates of the center of mass would be (1.82, 4.72).
However the solutions given are: (1.77, 4.23). Please help me figure out what I did wrong.
My attempt at a solution:
I divided the object into 3 different rectangles and found the coordinates for the center of mass of each one, considering the origin at point "O".
Then I found the mass of each rectangle, assuming the object has an area density of σ.
m1 = 15σ; m2= 6σ; m3 = 8σ.
After that I applied the center of mass position equation for x and y coordinates.
rx = (r1x*m1+r2x*m2+r3x*m3)/(m1+m2+m3) = (0.75*15σ+2.25*6σ+3.5*8σ)/(29σ) = 1.82
ry = (5*15σ + 9*6σ + 1*8σ)/(29σ) = 4.72
So the coordinates of the center of mass would be (1.82, 4.72).
However the solutions given are: (1.77, 4.23). Please help me figure out what I did wrong.