Three uniform thin rods, each of length L = 16 cm, form an inverted U. The vertical rods each have mass of 14 g; the horizontal rod has mass of 50 g. Where is the center of mass of the assembly (x, y)?
14 at y = 0 and 28 at y = 8 , total mass = 42
14 * 0 + 28* 8 = Ycg * 42
solve for Ycg
Xcg is in the middle of course
To find the center of mass of the assembly, we need to calculate the coordinates (x, y) where it is located.
Let's first find the center of mass of each component separately:
1. Vertical rods: Since both vertical rods have the same mass (14 g), their center of mass will lie at the midpoint of their length. So, the center of mass of the two vertical rods will be at (0, 8 cm) for the positive y-axis direction.
2. Horizontal rod: The horizontal rod has a mass of 50 g and is centered along the x-axis. So, the center of mass of the horizontal rod will be at (8 cm, 0) along the positive x-axis.
Next, we need to find the overall center of mass of the assembly by considering the center of mass of each component. Since the vertical rods are symmetrically placed with equal mass on either side of the y-axis, their center of mass (0, 8 cm) remains unchanged.
To find the overall x-coordinate of the center of mass, we consider the relative positions of the horizontal rod and the vertical rods. Since the horizontal rod is longer than the vertical rods, its mass has more influence on the overall x-coordinate. However, because the horizontal rod is balanced along the x-axis, its center of mass does not contribute to any displacement along the x-axis. Therefore, the overall x-coordinate of the center of mass remains at (0 cm).
Finally, to find the overall y-coordinate of the center of mass, we need to calculate the weighted average of the y-coordinates of the vertical rods based on their masses.
The total mass of the vertical rods is (14 g + 14 g) = 28 g, and their center of mass is at (0, 8 cm). Therefore, the y-coordinate of the center of mass is calculated as follows:
y-coordinate = (mass of first rod × y-coordinate of first rod + mass of second rod × y-coordinate of second rod) / total mass
= (14 g × 8 cm + 14 g × 8 cm) / 28 g
= 16 cm
So, the overall center of mass of the assembly is located at (0 cm, 16 cm).