The figure below shows a cubical box that has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length L = 39 cm.
(a) Find the x coordinate of the center of mass of the box.
(b) Find the y coordinate of the center of mass of the box. Ans:
(c) Find the z coordinate of the center of mass of the box. Ans:
X=2;y=35
To find the center of mass of the cubical box, we need to consider the uniform metal plate of negligible thickness from which it is constructed.
(a) To find the x coordinate of the center of mass, we need to consider the symmetry of the box. The box is symmetric in all three dimensions, so the center of mass will be at the midpoint of the x-axis. Since the box has an edge length of L = 39 cm, the x coordinate of the center of mass will be at x = L/2 = 39/2 = 19.5 cm.
(b) Similarly, to find the y coordinate of the center of mass, we again consider the symmetry of the box. The center of mass will be at the midpoint of the y-axis. Therefore, the y coordinate of the center of mass will be at y = L/2 = 39/2 = 19.5 cm.
(c) Finally, to find the z coordinate of the center of mass, we consider the symmetry once again. The center of mass will be at the midpoint of the z-axis. Therefore, the z coordinate of the center of mass will be at z = L/2 = 39/2 = 19.5 cm.
In summary, the center of mass of the cubical box is located at (19.5 cm, 19.5 cm, 19.5 cm) in the x, y, and z coordinates respectively.