A square of side 2L is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C’. The displacement of the x coordinate of the center of mass (from C to C’) is?
In the picture, C' moves up and to the right. So positive x and positive y direction.
To find the displacement of the x coordinate of the center of mass (from C to C'), we need to consider the mass distribution of the sandwich before and after the square is removed.
Before the square is removed, the mass is uniformly distributed across the entire square sandwich, so the center of mass (C) is located at the geometric center of the square.
After the square is removed, the mass distribution is different. We need to determine the new center of mass (C') of the remaining portion, which consists of four equal-sized triangular sections around the removed square.
To find the displacement of the x coordinate, we can divide the problem into two parts: the displacement of the x coordinate from C to the right edge of the removed square, and the displacement from the right edge of the removed square to C'.
1. Displacement from C to the right edge of the removed square:
The distance from C to the right edge of the square sandwich is L/2. However, since the removed square has a side length of 2L, it is located L/2 away from the right edge of the sandwich. Therefore, the displacement from C to the right edge of the removed square is L/2 - L/2 = 0.
2. Displacement from the right edge of the removed square to C':
Since the removed square has a side length of 2L, the distance from the right edge of the square to C' is L. Therefore, the displacement from the right edge of the removed square to C' is L.
Combining the two displacements, we find that the displacement of the x coordinate from C to C' is 0 + L = L.
So, the displacement of the x coordinate of the center of mass from C to C' is L.