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.
and the question is?
An archer pulls her bow string back 0.400 m by exerting a force that increases uniformly from zero to 232 N.
To find the center of mass of the plate, we need to consider the masses and positions of each component of the plate.
Given that the plate is square with side length L = 3.50 cm, its area A = L^2. Since the plate is uniform, the mass per unit area is constant, so the mass of the plate m = mass per unit area * A.
The mass of the removed squares can be calculated in a similar way. The side length of each removed square is L/4, so the area of each square is (L/4)^2. The mass of each removed square is the mass per unit area * (L/4)^2.
To find the center of mass of the plate, we need to consider the positions of each component. The position of the lower left corner of the plate is (0, 0). Since the plate is square, the center of mass of the plate will also be at the center of the plate.
So, to find the x-coordinate of the center of mass, we need to calculate the weighted average of the x-coordinates of the plate and the two removed squares. The x-coordinate of the center of mass of the plate is given by:
x_cm_plate = (m_plate * x_plate + m_square1 * x_square1 + m_square2 * x_square2) / (m_plate + m_square1 + m_square2)
Similarly, to find the y-coordinate of the center of mass, we need to calculate the weighted average of the y-coordinates of the plate and the two removed squares. The y-coordinate of the center of mass of the plate is given by:
y_cm_plate = (m_plate * y_plate + m_square1 * y_square1 + m_square2 * y_square2) / (m_plate + m_square1 + m_square2)
Now we can substitute the values and calculate the center of mass coordinates.