Answer to Question #162184 in Classical Mechanics for Darius

Question

If a fourth particle of mass 2.00kg is placed at x=0, y=0.250m in ex 1 find the x and y coordinates of the central gravity

Answer 1

Of course, the answer depends on the initial configuration of the three charges in ex.1. But to understand how to solve this problem, consider the simplest case with an equilateral triangle of three particles 2 kg each in its vertices. Assume the center of the triangle is at (0;0), then the x-coordinate of COG will not change. What will change, however, is the y-coordinate of the COG:

$$y_c=\frac{y_tm_t+y_4m_4}{m_t+m_4}=\\\space\\ =\frac{0\cdot(3\cdot2)+0.25\cdot2}{3\cdot2+2}=0.0625\text{ m}.$$