To find the x-coordinate of the center of mass for a two-dimensional shape on a grid, identify the centroid of each grid square, multiply each by its area, and sum these products. Divide this sum by the total area of the shape. The centroid of a square is at its center.
Step-by-step explanation:
To calculate the x-coordinate of the center of mass for a two-dimensional shape with uniform density, we must first consider the shape's geometry. Given that each grid square has a side length of d = 1.55 meters, we can calculate the area of each square. However, without a specific diagram, we'll assume a general approach. If the shape is composed of multiple grid squares, we would identify the centroid of each square and sum the products of their centroids' x-coordinates and their areas. We then divide this sum by the total area of the shape to find the x-coordinate of the center of mass. The formula is:
x_cm = (∑ x_i*a_i) / A_total
where x_i is the x-coordinate of the centroid of each square (which is simply the x-coordinate of the center of the grid square), a_i is the area of each square, and A_total is the total area of the shape.
Centroid of each square in a grid: For a square grid of side length d, the centroid's x-coordinate is located at d/2 from its left edge.
After calculating the x-coordinate of the center of mass using the formula above, we ensure that our answer is referenced from the origin, which is located at the bottom left corner of the diagram in the coordinate system provided.