Answer:
We can find the position of the center of mass of the system by using the formula:
Xcm = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4)
where Xcm is the x-coordinate of the center of mass, m1, m2, m3, and m4 are the masses of the point masses, and x1, x2, x3, and x4 are their respective x-coordinates.
Similarly, we can find the y-coordinate of the center of mass using the formula:
Ycm = (m1y1 + m2y2 + m3y3 + m4y4) / (m1 + m2 + m3 + m4)
where Ycm is the y-coordinate of the center of mass, m1, m2, m3, and m4 are the masses of the point masses, and y1, y2, y3, and y4 are their respective y-coordinates.
Let's label the masses and coordinates as follows:
m1 = 2kg, x1 = 0cm, y1 = 0cm
m2 = 4kg, x2 = 2cm, y2 = 0cm
m3 = 6kg, x3 = 2cm, y3 = 2cm
m4 = 8kg, x4 = 0cm, y4 = 2cm
Substituting these values into the formulas, we get:
Xcm = (2kg x 0cm + 4kg x 2cm + 6kg x 2cm + 8kg x 0cm) / (2kg + 4kg + 6kg + 8kg) = 2cm
Ycm = (2kg x 0cm + 4kg x 0cm + 6kg x 2cm + 8kg x 2cm) / (2kg + 4kg + 6kg + 8kg) = 1cm
Therefore, the center of mass of the system is located 2cm from corner A in the x-direction and 1cm from corner A in the y-direction.
Step-by-step explanation: