Particles of mass \(m, 2 m\), and \(3 m\) are arranged as shown in Figure P13.8, far from any other objects. These three particles interact only gravitationally, so that each particle experiences a vector sum of forces due to the other two. Call these \(\vec{F}_{m}, \vec{F}_{2 m}\), and \(\vec{F}_{3 m}\).

(a) Show that the lines of action of \(\vec{F}_{m}, \vec{F}_{2 m}\), and \(\vec{F}_{3 m}\) intersect at a common point.

(b) Is this point of intersection the center of mass of the system?

(c) Is the analysis of the motion of this system straightforward?

Data from Figure P13.8

Transcribed Image Text:

V5d d 2m 3m -2d-