A uniform, square metal plate with side L = 3.50 cm and mass 0.087 kg is located with its lower left corner at (x, y) = (0, 0) as shown in the figure. Two squares with side length L/4 are removed from the plate.
(a) What is the x-coordinate of the center of mass?
= L/2
(b) What is the y-coordinate of the center of mass?
To determine the y-coordinate of the center of mass, we need to analyze the distribution of mass along the y-axis.
The square plate has a side length of L = 3.50 cm. Two squares with a side length of L/4 are removed, leaving behind a smaller square plate with a side length of 3L/4.
The y-coordinate of the center of mass for the larger square plate can be determined by finding the midpoint along the y-axis of the larger plate.
Since the plate is positioned with its lower left corner at (x, y) = (0, 0), the origin of the coordinate system coincides with the lower left corner of the larger plate.
Therefore, the y-coordinate of the center of mass is located at half the side length of the larger plate, or (3L/4)/2 = 3L/8.
Substituting L = 3.50 cm into the equation, we get:
y-coordinate of the center of mass = (3(3.50 cm)/4)/2 = 1.3125 cm.
To find the y-coordinate of the center of mass, we need to consider the distribution of mass along the y-axis.
In this case, we have a square plate with two smaller squares removed from it. The remaining mass is distributed uniformly across the plate.
Since the plate is symmetric about the x-axis, the center of mass will be located at the midpoint of the plate along the y-axis.
Given that the side length of the plate is L = 3.50 cm, the center of mass will be located at y = L/2.
Thus, the y-coordinate of the center of mass is 3.50 cm / 2 = 1.75 cm.