A 3.0-kg mass is located at (0.0 m,8.0 m),and a 1.0-kg mass is located at (12 m,0.0 m).You want to add a 4.0-kg mass so that the center of mass (or center of gravity)of the three-mass system will be at the origin.What should be the coordinates of the 4.0-kg mass?
A)(-3.0 m,-6.0 m)
B)(-12 m,-8.0 m)
C)(3.0 m,6.0 m)
D)(-6.0 m,-3.0 m)

Question

Quizplus · Accepted Answer

The center of mass (CM) of a system can be found using the formula: $x_{CM} = \frac{\sum m_ix_i}{\sum m_i}$ and $y_{CM} = \frac{\sum m_iy_i}{\sum m_i}$ for the x and y coordinates, respectively. For the CM to be at the origin, both $x_{CM}$ and $y_{CM}$ must be 0. Given masses and their coordinates, and setting the desired CM at (0,0), we solve for the coordinates of the 4.0-kg mass. Plugging in the given values and solving the equations $0 = \frac{(3.0)(0) + (1.0)(12) + (4.0)x}{3.0 + 1.0 + 4.0}$ and $0 = \frac{(3.0)(8) + (1.0)(0) + (4.0)y}{3.0 + 1.0 + 4.0}$ leads to the solution for the coordinates of the 4.0-kg mass, which are (-3.0 m, -6.0 m).

A 30-Kg Mass Is Located at (0