Final answer:
To calculate the moment and center of mass for a system of point-masses, you need to multiply each mass by its distance from the reference point and sum these values for the moment, and weight their positions by their masses for the center of mass.
Step-by-step explanation:
The objective is to find the moment (m) of a system of point-masses and their center of mass (x). The moment is found by choosing a reference point (in this case, the origin) and summing the product of the mass and distance from the reference point for each mass.
The center of mass is the point where the mass of the system can be thought to be concentrated and is calculated as the weighted average of the positions of the masses.
The moment about the origin (m) is calculated as:
- m1 * distance of m1 from the origin + m2 * distance of m2 from the origin + m3 * distance of m3 from the origin.
The center of mass (x) is calculated as:
- (m1 * x1 + m2 * x2 + m3 * x3) / (m1 + m2 + m3).
To answer the specific question for the given masses (m1 = 15, m2 = 15, m3 = 30) and their distances from the origin, you would need the given positions of each mass. Once you have that information, you can use the above formulas to find the moment and the center of mass.